期刊：
Journal of Pure and Applied Algebra,2023年227(7):107322 ISSN：0022-4049
通讯作者：
Chengkang Xu
作者机构：
[Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xu, Chengkang] Shangrao Normal Univ, Shangrao, Jiangxi, Peoples R China.
通讯机构：
[Chengkang Xu] S;Shangrao Normal University, Shangrao, Jiangxi, China
摘要：
This paper studies restricted modules of gap-p Virasoro algebra g(p) and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted g(p)-modules of level (l) under bar and the category of twisted modules of vertex algebra V-Np((l) under bar, 0), where N-p is a new Lie algebra, (l) under bar :=(l(0), 0, center dot center dot center dot, 0) is an element of C[p/2]+1, l(0) is an element of C is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted g(p)-modules of level (l) under bar. More explicitly, we give a uniform construction of simple restricted g(p)-modules as induced modules. We present several equivalent characterizations of simple restricted g(p)-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of g(p). Moreover, simple restricted g(p)-modules of level (l) under bar are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted g(p)-modules of level (l) under bar (including Whittaker modules). (c) 2023 Elsevier B.V. All rights reserved.
期刊：
Journal of Algebra,2023年636:42-74 ISSN：0021-8693
通讯作者：
Wang, Q
作者机构：
[Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Guo, Hongyan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Haisheng] Rutgers State Univ, Dept Math Sci, Camden, NJ 08102 USA.;[Wang, Qing; Tan, Shaobin] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
通讯机构：
[Wang, Q ] X;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
摘要：
In this paper, we study a family of infinite-dimensional Lie algebras X ⠂S, where X stands for the type: A, B, C, D, and S is an abelian group, which generalize the A, B, C, D series of trigonometric Lie algebras. Among the main results, we identify X ⠂S with what are called the covariant algebras of the affine Lie algebra L ⠃S with respect to some automorphism groups, where LS is an explicitly defined associative algebra X ⠂S- viewed as a Lie algebra. We then show that restricted modules of level $ naturally correspond to equivariant quasi modules for affine vertex algebras related to LS. Furthermore, for any finite cyclic group S, we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types.& COPY; 2023 Elsevier Inc. All rights reserved.
期刊：
Mathematical Methods in the Applied Sciences,2023年46(5):5099-5118 ISSN：0170-4214
通讯作者：
Hangzhou Hu<&wdkj&>Hangzhou Hu Hangzhou Hu Hangzhou Hu
作者机构：
[Hu, Hangzhou; Zhao, Dun] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China.;[Li, Yuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Hangzhou Hu; Hangzhou Hu Hangzhou Hu Hangzhou Hu] S;School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 Gansu, China
关键词：
asymptotic behavior;ground states;NLS equations;periodic magnetic field;variational methods for second-order elliptic equations;XFEL Schrodinger equation
摘要：
We consider the following X‐ray free electron lasers Schrödinger equation (i∇−A)2u+V(x)u−μ|x|u=1|x|∗|u|2u−K(x)|u|q−2u,x∈ℝ3,$$ {\left(i\nabla -A\right)}&#x0005E;2u&#x0002B;V(x)u-\frac{\mu }{\mid x\mid }u&#x0003D;\left(\frac{1}{\mid x\mid}\ast {\left&#x0007C;u\right&#x0007C;}&#x0005E;2\right)u-K(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{q-2}u,x\in {\mathbb{R}}&#x0005E;3, $$ where A∈Lloc2(ℝ3,ℝ3)$$ A\in {L}_{loc}&#x0005E;2\left({\mathbb{R}}&#x0005E;3,{\mathbb{R}}&#x0005E;3\right) $$ denotes the magnetic potential such that the magnetic field B=curlA$$ B&#x0003D;\operatorname{curl}\kern0.4em A $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$‐periodic, μ∈ℝ,K∈L∞ℝ3$$ \mu \in \mathbb{R},K\in {L}&#x0005E;{\infty}\left({\mathbb{R}}&#x0005E;3\right) $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$ periodic and non‐negative, q∈(2,4)$$ q\in \left(2,4\right) $$. Using the variational method, based on a profile decomposition of the Cerami sequence in HA1ℝ3$$ {H}_A&#x0005E;1\left({\mathbb{R}}&#x0005E;3\right) $$, we obtain the existence of the ground state solution for suitable μ≥0$$ \mu \ge 0 $$. When μ<0$$ \mu &lt;0 $$ is small, we also obtain the non‐existence. Furthermore, we give a description of the asymptotic behavior of the ground states as μ→0+$$ \mu \to {0}&#x0005E;{&#x0002B;} $$.
作者机构：
[Li, Shuchao; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Shuchao Li] H;Hubei Key Laboratory of Mathematical Science, and Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Second largest eigenvalue;Spectral radius;Spectral Turán type problem;{C3,C5}-free graph
摘要：
In this paper we consider the extremal problem on adjacency spectral radius of {C-3, C-5}-free graphs. Assume that G is a graph with m edges having no isolated vertices, and let lambda be the spectral radius of its adjacency matrix. Firstly, by using the method of characterizing {C-3, C-5}-free non-bipartite graphs whose second largest eigenvalue is less than 4 root 5, we show that, if G is a {C-3, C-5}-free non-bipartite graph of size m, then [GRAPHICS] . Equality holds if and only if G congruent to C-7, where d(u) is the degree of vertex u and f denotes the number of 4-cycles in G. Secondly, we show that, if G is a {C-3, C-5}-free non-bipartite graph of odd size m, then lambda <= theta(m) with equality if and only if G congruent to RK2, m-3/2, where theta(m) is the largest root of chi(4) - chi(3) - (m - 3)chi(2) + (m - 4)chi + m - 5 = 0 and RK2, m-3/2 is obtained by replacing an edge of the complete bipartite graph K-2,K- m-3/2 with P5. (c) 2023 Elsevier B.V. All rights reserved.
作者机构：
[Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Huihui; Zhang, HH] Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
通讯机构：
[Zhang, HH ] L;Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
摘要：
Given a graph G and a real number alpha is an element of[0, 1], Nikiforov (2017) proposed the A(alpha)-matrix of Gas A(alpha)(G) = alpha D(G) +(1 - alpha) A( G), where A(G) and D( G) are the adjacency matrix and the degree diagonal matrix of G, respectively. The largest eigenvalue of A(alpha)(G), written as lambda(alpha)(G), is called the A alpha-index of G. A set of cycles in a graph G is called independent if no two cycles in it have a common vertex in G. For n > 2k - 1, let S-n,S- 2k-1 be the join of a clique on 2k - 1vertices with an independent set of n - (2k - 1) vertices. The famous Erdos-Posa theorem shows that for k >= 2 and n >= 24k, every n-vertex graph G with at least (2k - 1)(n - k) edges contains kindependent cycles, unless G congruent to S-n,S- 2k-1. In this paper, we consider an A(alpha)-spectral version of this theorem. We show that for fixed k >= 1, 0 < alpha < 1and n >= 104k(3)/alpha(a)(1- alpha), if an n-vertex graph Gsatisfies lambda(alpha)(G) >= lambda(alpha)(S-n,S- 2k-1), then it contains kindependent cycles, unless G congruent to Sn, 2k-1. This extends the result of Zhai and Liu (2022), in which they obtained the adjacency spectral version of the Erd.os-Posa theorem. (c) 2023 Elsevier B.V. All rights reserved.
期刊：
Finite Fields and Their Applications,2023年89:102223 ISSN：1071-5797
通讯作者：
Miao, Shujing(sjmiao2020@sina.com)
作者机构：
[Miao, Shujing; Wang, Junming; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Shujing Miao] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Cospectral graphs;Determined by generalized skew spectrum;Skew-adjacency matrix;Smith Normal Form
摘要：
Spectral characterization of graphs is an important topic in spectral graph theory. An oriented graph G(sigma) is obtained from a simple undirected graph G by assigning to every edge of G a direction so that G(sigma) becomes a directed graph. The skew-adjacency matrix of an oriented graph G(sigma) is a real skew-symmetric matrix S(G(sigma)) = (s(ij)), where s(ij) = -s(ji) = 1 if (i, j) is an arc; s(ij) = s(ji) = 0 otherwise. Let G(sigma) and H-tau be two oriented graphs whose skew-adjacency matrices are S(G(sigma)) and S(H-tau), respectively. We say G(sigma) is R-cospectral to H-tau if tJ - S(G(sigma)) and tJ - S(H-tau) have the same spectrum for any t is an element of R, where J is the all-ones matrix. An oriented graph G(sigma) is said to be determined by the generalized skew spectrum (DGSS for short), if any oriented graph which is R-cospectral to G(sigma) is isomorphic to G(sigma). Let W(G(sigma)) = [e, S(G(sigma))e, S-2(G(sigma))e, . . . , Sn-1(G(sigma))e] be the skew-walk-matrix of G(sigma), where e is the all-ones vector. A theorem of Qiu, Wang and Wang [9] states that if G(sigma) is a self-converse oriented graph and 2(-(sic)n/2(sic)) det W(G(sigma)) is odd and square-free, then G(sigma) is DGSS. In this paper, based on the Smith Normal Form of the skew-walk-matrix of G(sigma) we obtain our main result: Let q be a prime and G(sigma) be a self-converse oriented graph on n vertices with det W(G(sigma)) not equal 0. Assume that rank(q)(W(G(sigma))) = n - 1 if q is an odd prime, and rank(q)(W(G(sigma))) = (sic)n/2(sic) if q = 2. If Q is a regular rational orthogonal matrix satisfying Q(T)S(G(sigma))Q = S(H-tau) for some oriented graph H-tau, then the level of Q divides d(n)(W(G(sigma)))/q, where d(n)(W(G(sigma))) is the n-th invariant factor of q W(G(sigma)). Consequently, it leads to an easier way to prove Qiu, Wang and Wang's theorem above. (c) 2023 Elsevier Inc. All rights reserved.
摘要：
The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we apply the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.
期刊：
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE,2023年:- ISSN：0319-5724
通讯作者：
Liu, YY
作者机构：
[Jin, Shaojia; Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Jin, Shaojia] Wuhan Text Univ, Sch Math & Phys Sci, Wuhan 430200, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Sun, Jianguo] Univ Missouri, Dept Stat, Columbia, MO USA.
通讯机构：
[Liu, YY ] W;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
摘要：
Abstract This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure. Résumé Cet article traite de l'estimation non paramétrique d'une fonction de survie en présence d'erreurs de mesure lors de l'observation du temps de défaillance d'intérêt. Une situation où de telles problématiques se posent fréquemment est celle des études cliniques sur les maladies chroniques, où l'observation du temps écoulé jusqu'à l'événement de défaillance d'intérêt, tel que l'apparition de la maladie, repose sur la mémoire du patient ou sur l'examen des dossiers médicaux électroniques. Il est évident que ces deux contextes sont sujets à des erreurs de mesure. Pour résoudre ce défi, les auteurs de cet article proposent une approche d'extrapolation par simulation visant à corriger le biais induit par l'erreur de mesure. Afin de surmonter d'éventuelles complexités computationnelles, ils utilisent la régression spline pour approximer la fonction de coefficient extrapolée non spécifiée en fonction du temps, tout en établissant les propriétés asymptotiques de l'estimateur proposé. Cette méthode est ensuite appliquée à l'estimation non paramétrique basée sur des données censurées par intervalles. Des expérimentations numériques approfondies, incluant à la fois des jeux de données simulés et des données d'études réelles, mettent en évidence la faisabilité de cette procédure d'estimation proposée.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年44(1):182-204 ISSN：1078-0947
通讯作者：
Guo, YJ
作者机构：
[Li, Yan; Guo, Yujin; Liang, Wenning] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
关键词：
The planar Schrodinger-Poisson system;constraint minimizers;loga-rithmic potentials;asymptotic expansions;refined spike profiles
摘要：
This paper is concerned with constraint minimizers of the planar Schrodinger-Poisson system with a logarithmic convolution potential and a logarithmic external potential V (x) = ln(1+|x|(2)). It is known that minimizers exist if and only if the particle mass p > 0 satisfies p < p* for some threshold p* is an element of(0, infinity). As a continuation of [22], this paper is devoted to analyzing the refined spike profiles of constraint minimizers as p NE arrow p*.
作者机构：
[Liu, Ning; Jiang, Anguo] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China.;[Jing, Naihuan] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;[Jing, Naihuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, USA<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
We study the Q-Kostka polynomials
$$L_{\lambda \mu }(t)$$
by the vertex operator realization of the Q-Hall–Littlewood functions
$$G_{\lambda }(x;t)$$
and derive new formulae for
$$L_{\lambda \mu }(t)$$
. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials
$$Y^{\lambda }_{\mu }(t)$$
as both an analogue of the Green polynomials and deformation of the spin irreducible characters of
$$\mathfrak S_n$$
. Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of
$$Y^{\lambda }_{\mu }(t)$$
are included for
$$n\le 7.$$
作者：
Liu, C. H. U. A. N. G. Y. E.;Nguyen, N. G. H. I. E. M., V
期刊：
COMMUNICATIONS IN MATHEMATICAL SCIENCES,2023年21(3):641-669 ISSN：1539-6746
通讯作者：
Liu, C.
作者机构：
[Liu, C. H. U. A. N. G. Y. E.] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Liu, C. H. U. A. N. G. Y. E.] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.;[Nguyen, N. G. H. I. E. M., V] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA.
通讯机构：
[Liu, C.] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, P.O. Box 71010, China
关键词：
abcd-system;BBMequation;Euler equations;KdV-equation;linear Schrödinger equation;NLS-equation;NLS-KdV system
摘要：
In this paper, we consider the following logarithmic Schrödinger equation $ \begin{equation*} -\varepsilon^2\Delta u + V(x)u = u\log u^2\ \ \text{in}\ {\mathbb R}^N, \end{equation*} $ where $ \varepsilon>0 $, $ N\ge 1 $, $ V(x)\in C({\mathbb R}^N, {\mathbb R}) $ is a continuous potential which can be unbounded below. By variational methods and penalized idea, we show that the problem has a family of solutions $ u_{\varepsilon} $ concentrating at any finite given local minima of $ V $. Our results generalize the single peak case in [36] to the multi-peak case but the penalization in this paper is different.
期刊：
Journal of Functional Analysis,2023年284(6):109820 ISSN：0022-1236
通讯作者：
Ting Zhou
作者机构：
[Lu, Zheng-Yi; Liu, Jinsong] Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China.;[Liu, Jinsong] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China.;[Zhou, Ting] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Ting Zhou] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
摘要：
Let mu = mu{Rn,Bn} = delta R-1 1 B1 * delta(R2R1)-1B2 * .. . be a Borel probability measure with a compact support, where Rn E M2(Z), BnC Z2 and (Rn, Bn, Ln) forms a Hadamard triple for all n > 1. In this paper, we consider the existence of exponential orthogonal basis in L2(mu). We extend the concept of equi-positive family in [1] to higher dimensions, and provide a new idea to characterize the spectrality of such measures. In details, we study the spectrality and non-spectrality of Moran-Sierpinski type measures specifically under some necessary assumptions. The partial findings of several previous studies are extended by this study, such as Cantor-Moran measures (An-Fu-Lai [1], An-He-He [3]), Moran-Sierpinski type measures (Wang-Dong [47]) and Moran-Cantor-Dust type measures (Chen-Liu-Su-Wang [9]).(c) 2022 Elsevier Inc. All rights reserved.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-9 ISSN：0126-6705
通讯作者：
Meng Fai Lim
作者机构：
[Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Meng Fai Lim] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
关键词：
Norm principle;Norm maps;Even K-groups;Finite extensions of number fields
摘要：
We investigate the norm maps of algebraic even K-groups of finite extensions of number fields. Namely, we show that they are surjective in most situations. In the event that they are not surjective, we give a criterion in determining when an element in the even K-group of the base field comes from a norm of an element from the even K-groups of the extension field. This latter criterion is only reliant on the real primes of the base field.
摘要：
Let $M=(\begin {smallmatrix}\rho ^{-1} & 0 \\0 & \rho ^{-1} \\\end {smallmatrix})$ be an expanding real matrix with $0<\rho <1$, and let ${\mathcal D}_n=\{(\begin {smallmatrix} 0\\ 0 \end {smallmatrix}),(\begin {smallmatrix} \sigma _n\\ 0 \end {smallmatrix}),(\begin {smallmatrix} 0\\ \gamma _n \end {smallmatrix})\}$ be digit sets with $\sigma _n,\gamma _n\in \{-1,1\}$ for each $n\ge 1$. Then the infinite convolution\n$$ \begin{align*}\mu_{M,\{{\mathcal D}_n\}}=\delta_{M^{-1}{\mathcal D}_1}\ast\delta_{M^{-2}{\mathcal D}_2}\ast\cdots\end{align*} $$\nis called a Moran–Sierpinski measure. We give a necessary and sufficient condition for $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ to admit an infinite orthogonal set of exponential functions. Furthermore, we give the exact cardinality of orthogonal exponential functions in $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ when $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ does not admit any infinite orthogonal set of exponential functions based on whether $\rho $ is a trinomial number or not.
作者机构：
[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
This paper is concerned with the inverse scattering problem of determining the unknown coefficients for a nonlinear two-dimensional Schrodinger equation. We establish for the first time the increasing stability of the inverse scattering problem from the multi-frequency far-field pattern for nonlinear equations. To achieve this goal, we prove the existence of a holomorphic region and an upper bound for the solution with respect to the complex wavenumber, which also leads to the well-posedness of the direct scattering problem. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the unknown coefficients, where the latter decreases as the upper bound of the frequency increases.& COPY; 2023 Elsevier B.V. All rights reserved.
作者机构：
[Xie, Minghong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Tan, Zhong] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;[Tan, Zhong] Xiamen Univ, Shenzhen Res Inst, Shenzhen 518057, Peoples R China.
通讯机构：
[Tan, Z ] X;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;Xiamen Univ, Shenzhen Res Inst, Shenzhen 518057, Peoples R China.
关键词：
spatiotemporal EIT problem;fractional Dirichlet-to-Neumann operator;critical exponent;bubbling phenomena
摘要：
We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent. There are three major ingredients in this paper. The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value. The second ingredient is the Lq(2 ≤ q < ∞) estimate of the global solution applying the Moser iteration, which allows us to show that any global solution is a classical solution. The third, which is the main ingredient of this paper, explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.
作者：
Selima, Ehab S.;Abu-Nab, Ahmed K.;Morad, Adel M.
期刊：
Mathematical Methods in the Applied Sciences,2023年 ISSN：0170-4214
通讯作者：
Morad, AM
作者机构：
[Abu-Nab, Ahmed K.; Morad, Adel M.; Selima, Ehab S.] Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm, Egypt.;[Selima, Ehab S.] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Abu-Nab, Ahmed K.; Selima, Ehab S.] Acad Sci Res & Technol ASRT, Cairo, Egypt.;[Abu-Nab, Ahmed K.] Moscow Inst Phys & Technol, Phystech Sch Appl Math & Informat, Dolgoprudnyi, Russia.;[Morad, Adel M.] Univ Sadat City, Fac Comp & Artificial Intelligence, Sadat City, Egypt.
通讯机构：
[Morad, AM ] M;Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm 32511, Egypt.
摘要：
The ( 2 + 1 ) $$ \left(2+1\right) $$ -dimensional coupled cubic–quintic complex Ginzburg–Landau equations ( ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs) can simulate a variety of binary fluid thermal convection characteristics, containing complex parameters. The analysis of pattern formation in chaotic and nonlinear dynamical systems can benefit greatly from the use of this thermal convection model. The primary goal of this study is to find analytical solutions for some recent advances that have been made for Rayleigh–Bénard convection by applying the ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs model for slowly varying spatio-temporal amplitudes of the wave motion. In addition, novel traveling solitary wave solutions for the model equation are derived using a very useful method to investigate how complex physical coefficients affect the profiles of propagating waves. Furthermore, we introduce the WTC-Kruskal algorithm of the Painlevé methodology to examine the integrability of the ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs and the truncated Painlevé expansion is used to extract the Bäcklund transform, from which new solitary solutions can be acquired. The results also demonstrated a good agreement with previous works and were more significant and accurate in two and three dimensions of the proposed model. Finally, the computational results indicate that the effects of the physical parameters of the considered equations can be demonstrated by utilizing 2D and 3D graphics for different values of these parameters.
期刊：
Journal of Fixed Point Theory and Applications,2023年25(2):1-31 ISSN：1661-7738
通讯作者：
Wang, CH
作者机构：
[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.;[Wang, Qingfang] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.;[Yang, Jing] Jiangsu Univ Sci & Technol, Sch Sci, Zhenjiang 212003, Peoples R China.
通讯机构：
[Wang, CH ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
摘要：
We study the following nonlinear critical elliptic equation
$$\begin{aligned} -\Delta u+\epsilon Q(y)u=u^{\frac{N+2}{N-2}},\;\;\; u>0\;\;\;\hbox { in } {\mathbb {R}}^N, \end{aligned}$$
where
$$\epsilon >0$$
is small and
$$N\ge 5.$$
Assuming that Q(y) is periodic in
$$y_1$$
with period 1 and has a local minimum at 0 satisfying
$$Q(0)>0,$$
we prove the existence and local uniqueness of infinitely many bubbling solutions of it. This local uniqueness result implies that some bubbling solutions preserve the symmetry of the potential function Q(y), i.e., the bubbling solution whose blow-up set is
$$\{(jL,0,\ldots ,0):j=0,\pm 1, \pm 2,\ldots , \pm m\}$$
must be periodic in
$$y_{1}$$
provided that
$$\epsilon $$
goes to zero and L is any positive integer, where m is the number of the bubbles which is large enough but independent of
$$\epsilon .$$
作者：
Chen, Haixia;Wang, Chunhua;Xie, Huafei;Zhou, Yang
期刊：
ANNALI DI MATEMATICA PURA ED APPLICATA,2023年 ISSN：0373-3114
通讯作者：
Wang, CH
作者机构：
[Chen, Haixia] Hanyang Univ, Coll Nat Sci, Dept Math, 222 Wangsimni Ro, Seoul 04763, South Korea.;[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xie, Huafei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.;[Zhou, Yang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, CH ] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Critical Sobolev exponents;Non-degeneracy;Local Pohozaev identities;Green's function
摘要：
We revisit the well-known Brezis-Nirenberg problem {- Delta u = u (N+2/N-2) + epsilon u, in Omega, u > 0, in Omega, u = 0, on partial derivative Omega, where epsilon > 0 and Omega subset of RN are a smooth bounded domain with N >= 3. The existence of multi-bump solutions to above problem for small parameter epsilon > 0 was obtained by Musso and Pistoia (Indiana Univ Math J 51:541-579, 2002). However, to our knowledge, whether themulti-bump solutions are non-degenerate that is open. Here, we give some straightforward answer on this question under some suitable assumptions for the Green's function of - Delta in Omega, which enriches the qualitative analysis on the solutions of Brezis-Nirenberg problem and can be viewed as a generalization of Grossi (Nonlinear Differ Equ Appl 12:227-241, 2005) where the non-degeneracy of a single-bump solution has been proved. And the main idea is the blow-up analysis based on the local Pohozaev identities.
