Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index

被引：39

作者：

Medeiros, Everaldo ^{[2
]}

Perera, Kanishka ^{[1
]}

机构：

[1] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 09期

关键词：

p-Laplacian; Boundary value problems; Concave-convex nonlinearities; Multiple solutions; Cohomological index; Cohomological linking; LOCAL MINIMIZERS; EQUATIONS; NONLINEARITIES; SOBOLEV; CONCAVE;

D O I：

10.1016/j.na.2009.02.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a quasilinear elliptic problem with the Dirichlet boundary condition in a bounded domain involving the operator Au = -Delta(p)u - Delta(q)u. Assuming that the nonlinearity has a concave-convex behavior we obtain some multiplicity results. More precisely, we obtain five nontrivial solutions; two by a minimization argument, two by the mountain pass theorem, and the other by a cohomological linking theorem. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：3654 / 3660

页数：7

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