期刊：
ADVANCES IN DIFFERENTIAL EQUATIONS,1997年2(3):361-382 ISSN：1079-9389
作者机构：
Department of Mathematics, Huazhong Normal University, Wuhan, 430070, China;Department of Mathematics, University of Rochester, Rochester, NY 14627, United States;Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States;[Yinbing Y.] Department of Mathematics, Huazhong Normal University, Wuhan, 430070, China, Department of Mathematics, University of Rochester, Rochester, NY 14627, United States;[Li Y.] Department of Mathematics, University of Rochester, Rochester, NY 14627, United States, Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States
关键词：
In this paper;we consider the semilinear elliptic problem $$ -\triangle u+ u=|u|^{p-2}u+ \mu f(x);\quad u \in H^1(\Bbb R^N);\quad N>2. \tag"$(*)_\mu$" $$ For $p> 2$;we show that there exists a positive constant $\mu ^*>0$ such that $(*)_\mu$ possesses a minimal positive solution if $\mu \in (0;\mu ^*)$ and no positive solutions if $\mu > \mu^*$. Furthermore;if $p< \frac{2N}{N-2}$;then $(*)_\mu$ possesses at least two positive solutions for $\mu \in (0;\mu^{*})$;a unique positive solution if $\mu =\mu^*$ and there exists a constant $\mu _{*} >0 $ such that when $ \mu\in (0;\mu_{*})$;problem $(*)_\mu$ possesses at least three solutions. We also obtain some bifurcation results of the solutions at $\mu =0$ and $\mu=\mu^*$. Published: 1997 First available in Project Euclid: 23 April 2013 zbMATH: 1023.35503 MathSciNet: MR1441848 Digital Object Identifier: 10.57262/ade/1366742248 Subjects: Primary: 35J60 Secondary: 35B05;35B32
摘要：
In this paper, we consider the semilinear elliptic problem $$ -\triangle u+ u=|u|^{p-2}u+ \mu f(x), \quad u \in H^1(\Bbb R^N), \quad N>2. \tag"$(*)_\mu$" $$ For $p> 2$, we show that there exists a positive constant $\mu ^*>0$ such that $(*)_\mu$ possesses a minimal positive solution if $\mu \in (0, \mu ^*)$ and no positive solutions if $\mu > \mu^*$. Furthermore, if $p< \frac{2N}{N-2}$, then $(*)_\mu$ possesses at least two positive solutions for $\mu \in (0, \mu^{*})$, a unique positive solution if $\mu =\mu^*$ and there exists a constant $\mu _{*} >0 $ such that when $ \mu\in (0, \mu_{*})$, problem $(*)_\mu$ possesses at least three solutions. We also obtain some bifurcation results of the solutions at $\mu =0$ and $\mu=\mu^*$.
摘要：
In this paper we prove that there exist 4-{v, k, k, k, k; lambda} supplementary difference sets with v = q(2), q = 3(mod 8) a prime power, k = q(q - 1)/2, lambda = 4k - v, and Hadamard matrices of order 4v.
摘要：
In this paper, the absolute stability of control systems with multi nonlinear feedback terms are studied. The sufficient and necessary conditions of absolute stability are obtained. Some applied sufficient conditions of absolute stability are given.
期刊：
Journal of Differential Equations,1996年130(1):179-200 ISSN：0022-0396
通讯作者：
Deng, YB
作者机构：
[Li, Y; Deng, YB] UNIV ROCHESTER,DEPT MATH,ROCHESTER,NY 14627.;[Deng, YB] HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
通讯机构：
[Deng, YB] H;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
摘要：
In this paper, we consider the semilinear elliptic equation (*)(mu) -Delta u + u = u(p-1) + uf(x), u > 0, u is an element of H-1 (R(N)), N > 2. For p = 2N/(N - 2), we show that there exists a positive constant mu* > 0 such that (*)(mu) possesses at least one solution if mu is an element of (0, mu*) and no solutions if mu > mu*. Furthermore, (*)(mu) possesses a unique solution when mu = mu*, and at least two solutions when mu is an element of (0, mu*) and 2 < N < 6. For N greater than or equal to 6, under some monotonicity conditions on f ((1.6)) we show that there exist two constants 0 < mu** less than or equal to mu** < mu* such that problem (*)(mu) possesses a unique solution for mu is an element of (0, mu**), and at least two solutions if mu is an element of (mu**, mu*). (C) 1996 Academic Press, Inc.
期刊：
Applied Mathematics and Computation,1996年75(2-3):103-115 ISSN：0096-3003
通讯作者：
Liao, XX
作者机构：
[Li, J] Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, United States;[Liao, XX] Department of Mathematics, Huazhong Normal University, Wuhan, Hubei, China
通讯机构：
[Liao, XX ] ;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN,HUBEI,PEOPLES R CHINA.
关键词：
Global stability;Sufficient conditions;Matrices
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,1996年126(4):719-724 ISSN：0308-2105
通讯作者：
Zhu, CJ
作者机构：
[Zhu, CJ] Department of Mathematics, Central China Normal University, Wuhan 430070, P.R. China
通讯机构：
[Zhu, CJ] C;CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
摘要：
In this paper we prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 hyperbolic conservation laws, which is neither necessarily strictly hyperbolic nor necessarily genuinely nonlinear.
期刊：
Journal of Computational and Applied Mathematics,1996年69(2):367-377 ISSN：0377-0427
通讯作者：
Li, J.-L.
作者机构：
[Li, JL] UNIV WITWATERSRAND,DEPT MATH,WITWATERSRAND 2050,SOUTH AFRICA.;[Li, JL] CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 4300
通讯机构：
Department of Mathematics, Central China Normal University, China
关键词：
quasi-regular c-fraction;order of meromorphic function
摘要：
We investigate the growth of the meromorphic function defined by [GRAPHICS] where a(i) are complex numbers, a(i) not equal 0, \a(i)\ greater than or equal to \a(i+1)\(i = 1,2, ...) and lim(1-->infinity) a(i) = 0. b is a complex number.
摘要：
In this paper we prove that for any prime power q equivalent to 3 (mod 8) there exist 4 - {q(2); k, k, k, k; lambda} supplementary difference sets (SDSs) with k = q(q - 1)/2, lambda 4k - q(2), and Hadamard matrices of order 4q(2), and give several constructions of these SDSs. Moreover, combining the results of reference [1], we conclude that for any prime p equivalent to 3 (mod 8) and integer r greater than or equal to 1 there exists an Hadamard matrix of order 4p(2r).
