Solutions with multiple peaks for nonlinear elliptic equations

被引：72
作者：
Cao, DM
Noussair, ES
Yan, SS
机构：
[1] Chinese Acad Sci, Wuhan Inst Math Sci, Phys Math Lab, Wuhan 430071, Peoples R China
[2] Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia
[3] S China Univ Technol, Dept Appl Math, Guangzhou 510641, Peoples R China
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 1999年 / 129卷
基金：
中国国家自然科学基金; 澳大利亚研究理事会;
关键词：
D O I：
10.1017/S030821050002134X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Solutions with peaks near the critical points of Q(x) are constructed for the problem -Delta u + lambda(2)u = Q(x)\u\(P-2)u, x is an element of R-N, u is an element of H-1 and 2 < p < (2N/(N - 2)). We establish the existence of 2(k) - 1 positive solutions when Q(x) has k non-degenerate critical points in R-N.
引用
收藏
页码：235 / 264
页数：30
相关论文
共 14 条
[1]  
[Anonymous], 1990, REV MAT IBEROAM, DOI DOI 10.4171/RMI/92
[2]   ON A VARIATIONAL PROBLEM WITH LACK OF COMPACTNESS - THE TOPOLOGICAL EFFECT OF THE CRITICAL-POINTS AT INFINITY [J].
BAHRI, A ;
LI, YY ;
REY, O .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1995, 3 (01) :67-93
[3]   ON A NONLINEAR ELLIPTIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT - THE EFFECT OF THE TOPOLOGY OF THE DOMAIN [J].
BAHRI, A ;
CORON, JM .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (03) :253-294
[4]   On the existence of a positive solution of semilinear elliptic equations in unbounded domains [J].
Bahri, A ;
Lions, PL .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (03) :365-413
[5]  
Bahri A., 1989, RES NOTES MATH, V182
[6]  
BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
[7]   POSITIVE SOLUTION AND BIFURCATION FROM THE ESSENTIAL SPECTRUM OF A SEMILINEAR ELLIPTIC EQUATION ON RN [J].
CAO, DM .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (11) :1045-1052
[8]   Multiplicity of positive and nodal solutions for nonlinear elliptic problems in R(N) [J].
Cao, DM ;
Noussair, ES .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1996, 13 (05) :567-588
[9]  
KWONG MK, 1989, ARCH RATION MECH AN, V105, P243
[10]  
Lions P.L., 1988, NONLINEAR DIFFUSION
12