Dirichlet problems with double resonance and an indefinite potential

被引：10

作者：

Gasinski, Leszek ^{[2
]}

Papageorgiou, Nikolaos S. ^{[1
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] Jagiellonian Univ, Inst Comp Sci, PL-30348 Krakow, Poland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 12期

关键词：

Constant sign and nodal solutions; Double resonance; Harnack inequality; Critical groups; Gradient flow; Mountain pass theorem; BOUNDARY-VALUE-PROBLEMS; CRITICAL-POINT THEORY; MULTIPLE SOLUTIONS; ELLIPTIC-EQUATIONS; MORSE-THEORY; P-LAPLACIAN; PERTURBATIONS;

D O I：

10.1016/j.na.2011.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider semilinear Dirichlet problems with an unbounded and indefinite potential and with a Caratheodory reaction. We assume that asymptotically at infinity the problem exhibits double resonance. Using variational methods, together with Morse theory and flow invariance arguments, we prove multiplicity theorems producing three, five, six or seven nontrivial smooth solutions. In most multiplicity theorems, we provide precise sign information for all the solutions established. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：4560 / 4595

页数：36

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