作者机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
关键词：
Schrodinger-Kirchhoff type equation;variational methods;multiple positive solutions;concentrating solution;penalization method
摘要：
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrodinger-Kirchhoff type -e~pM(e~(p-N)∫_R~N|∆pu+V(x)|u|~(p-2)u = f(u) in R~N, where Δ_p is the p-Laplacian operator, 1 < p < N, M: R~+ → R~+ and V:R~N →R~+ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik-Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
作者机构：
[Fan, Shilei] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Liao, Lingmin] Univ Paris Est Crteil Val de Marne, LAMA, F-94010 Creteil, France.
通讯机构：
[Fan, Shilei] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
关键词：
p-adic dynamical system;rational maps;minimal decomposition;subshift of finite type
摘要：
The dynamical structure of the rational map ax+1/x on the projective line
$$\mathbb{P}^1(\mathbb{Q}_2)$$
over the field ℚ2 of 2-adic numbers, is fully described.
作者机构：
[Feng, Hong Liang; Yao, Xiao Hua; Wang, Hua] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Yao, Xiao Hua; Wang, Hua] Cent China Normal Univ, Hubei Prov Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yao, Xiao Hua] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Prov Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.
关键词：
Fourth order NLS;potential;morawetz estimate;scattering
摘要：
Based on the endpoint Strichartz estimates for the fourth order Schrodinger equation with potentials for n ≥ 5 by [Feng, H., Soffer, A., Yao, X.: Decay estimates and Strichartz estimates of the fourth-order Schrodinger operator. J. Funct. Anal., 274, 605–658(2018)], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in [Pausader, B.: The cubic fourth-order Schrodinger equation. J. Funct. Anal., 256, 2473–2517(2009)]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity 1 + 8/n < p < 1 + 8/n-4 in dimensions n ≥ 7.
作者机构：
[Yan, Guozheng; Sun, Meiman] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Yan, Guozheng] Hubei Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yan, Guozheng] C;[Yan, Guozheng] H;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Hubei Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.
摘要：
In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system,we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.
作者机构：
[Cao, Daomin] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China.;[Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Peng, Shuangjie] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Yan, Shusen] Univ New England Armidale, Dept Math, Armidale, NSW 2351, Australia.
摘要：
In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {- Delta u = lambda Sigma(k)(j=1) 1(B delta(x0, j)) (u- k(j))(+)(p), in Omega, u = 0 on partial derivative Omega, where 0 < p < 1, Omega subset of R-2 is a bounded simply-connected smooth domain, k(i) (i = 1,..., k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x(0) = (x(0,1),..., x(0,k)) of the Kirchhoff-Routh function defined on Omega(k) corresponding to (k(1), ..., k(k)), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as lambda ->+infinity, the vorticity set {y : u(lambda) > k(j)} boolean AND B-delta(X-0,X-j) shrinks to {x(0,j)}, and the local vorticity strength near each x(0,j) approaches k(j), j = 1,..., k. This result makes the study of the above problem with p >= 0 complete since the cases p > 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.
摘要：
Let
$$\mathfrak{g} = W_1 $$
be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let
be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250: 473–484], we show that the variety
is reducible, and not equidimensional. Irreducible components of
and their dimensions are precisely given. As a consequence, the variety
is not normal.
作者机构：
[Li, Peiyan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Gu, Wei] Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Hubei, Peoples R China.
通讯机构：
[Gu, Wei] Z;Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Hubei, Peoples R China.
关键词：
Kolmogorov partial differential equations;transition probability density function;transition cumulative distribution function;compact difference scheme
摘要：
A method based on higher-order partial differential equation (PDE) numerical scheme are proposed to obtain the transition cumulative distribution function (CDF) of the diffusion process (numerical differentiation of the transition CDF follows the transition probability density function (PDF)), where a transformation is applied to the Kolmogorov PDEs first, then a new type of PDEs with step function initial conditions and 0, 1 boundary conditions can be obtained. The new PDEs are solved by a fourth-order compact difference scheme and a compact difference scheme with extrapolation algorithm. After extrapolation, the compact difference scheme is extended to a scheme with sixth-order accuracy in space, where the convergence is proved. The results of the numerical tests show that the CDF approach based on the compact difference scheme to be more accurate than the other estimation methods considered; however, the CDF approach is not time-consuming. Moreover, the CDF approach is used to fit monthly data of the Federal funds rate between 1983 and 2000 by CKLS model.
