Existence of solutions for a class of biharmonic equations with critical nonlinearity in

被引：0
作者：
Liang, Sihua [1 ,3 ]
Zhang, Jihui [2 ,4 ]
Luo, Yingyu [1 ]
机构：
[1] Changchun Normal Univ, Coll Math, Changchun 130032, Jilin, Peoples R China
[2] Nanjing Normal Univ, Inst Math, Sch Math & Comp Sci, Nanjing 210097, Jiangsu, Peoples R China
[3] Jilin Univ, Key Lab Symbol Computat & Knowledge Engn, Minist Educ, Changchun 130012, Peoples R China
[4] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210097, Jiangsu, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2016年 / 110卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Biharmonic equation; Critical nonlinearity; Variational method; Critical point; CONCENTRATION-COMPACTNESS PRINCIPLE; COMPETING POTENTIAL FUNCTIONS; DECAYING RADIAL POTENTIALS; CRITICAL SOBOLEV EXPONENTS; SCHRODINGER-EQUATIONS; BOUND-STATES; SEMICLASSICAL STATES; CRITICAL FREQUENCY; POSITIVE SOLUTIONS; STANDING WAVES;
D O I：
10.1007/s13398-015-0257-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the existence and multiplicity of solutions of biharmonic equations with critical nonlinearity in , . Under suitable assumptions, we prove that it has at least one solution and, if h(x, .) is odd, for any , it has at least m pairs of solutions.
引用
收藏
页码：681 / 693
页数：13
相关论文
共 39 条
[1]   On a class of singular biharmonic problems involving critical exponents [J].
Alves, CO ;
do O, JM ;
Miyagaki, OH .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 277 (01) :12-26
[2]   Nontrivial solutions for a class of semilinear biharmonic problems involving critical exponents [J].
Alves, CO ;
do O, JM ;
Miyagaki, OH .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (01) :121-133
[3]   Bound states of nonlinear Schrodinger equations with potentials vanishing at infinity [J].
Ambrosetti, A. ;
Malchiodi, A. ;
Ruiz, D. .
JOURNAL D ANALYSE MATHEMATIQUE, 2006, 98 (1) :317-348
[4]  
Ambrosetti A, 2005, DIFFER INTEGRAL EQU, V18, P1321
[5]  
Ambrosetti A, 2005, J EUR MATH SOC, V7, P117
[6]   Semiclassical states of nonlinear Schrodinger equations [J].
Ambrosetti, A ;
Badiale, M ;
Cingolani, S .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 140 (03) :285-300
[7]   Multiplicity results for some nonlinear Schrodinger equations with potentials [J].
Ambrosetti, A ;
Malchiodi, A ;
Secchi, S .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 159 (03) :253-271
[8]  
Ambrosetti A., 2006, , Progress in Mathematics
[9]   ON CRITICAL-POINT THEORY FOR INDEFINITE FUNCTIONALS IN THE PRESENCE OF SYMMETRIES [J].
BENCI, V .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 274 (02) :533-572
[10]   Existence and non existence of the ground state solution for the nonlinear Schroedinger equations with V(∞)=0 [J].
Benci, V ;
Grisanti, CR ;
Micheletti, AM .
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2005, 26 (02) :203-219
1234