Multiple nontrivial solutions for some fourth-order semilinear elliptic problems

被引:94
作者
Zhang, JH [1 ]
Li, SJ [1 ]
机构
[1] Nanjing Normal Univ, Sch Math & Comp Sci, Nanjing 210097, Peoples R China
关键词
critical group; homological nontrivial critical point; Morse theory; local linking; multiple solutions; travelling waves;
D O I
10.1016/j.na.2004.07.047
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the existence of multiple nontrivial solutions for some fourth order semilinear elliptic boundary value problems. The weak solutions are sought by means of Morse theory and local linking. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:221 / 230
页数:10
相关论文
共 12 条
[1]   ABSTRACT CRITICAL-POINT THEOREMS AND APPLICATIONS TO SOME NON-LINEAR PROBLEMS WITH STRONG RESONANCE AT INFINITY [J].
BARTOLO, P ;
BENCI, V ;
FORTUNATO, D .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (09) :981-1012
[2]   Critical point theory for asymptotically quadratic functionals and applications to problems with resonance [J].
Bartsch, T ;
Li, SJ .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (03) :419-441
[3]   ON THE SOLVABILITY OF DEGENERATED QUASI-LINEAR ELLIPTIC-EQUATIONS OF HIGHER-ORDER [J].
DRABEK, P ;
KUFNER, A ;
NICOLOSI, F .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) :325-347
[4]   LARGE-AMPLITUDE PERIODIC OSCILLATIONS IN SUSPENSION BRIDGES - SOME NEW CONNECTIONS WITH NONLINEAR-ANALYSIS [J].
LAZER, AC ;
MCKENNA, PJ .
SIAM REVIEW, 1990, 32 (04) :537-578
[5]   GLOBAL BIFURCATION AND A THEOREM OF TARANTELLO [J].
LAZER, AC ;
MCKENNA, PJ .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 181 (03) :648-655
[6]   Remarks on multiple nontrivial solutions for quasi-linear resonant problems [J].
Liu, J ;
Su, JB .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 258 (01) :209-222
[7]   Multiplicity results for a fourth-order semilinear elliptic problem [J].
Micheletti, AM ;
Pistoia, A .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 31 (07) :895-908
[8]   Nontrivial solutions for some fourth order semilinear elliptic problems [J].
Micheletti, AM ;
Pistoia, A .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 34 (04) :509-523
[9]  
Tarantello G., 1992, DIFFER INTEGRAL EQU, V5, P561
[10]   Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity [J].
Xu, GX ;
Zhang, JH .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (02) :633-640