Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian

被引：69

作者：

Filippakis, Michael E. ^{[1
]}

Papageorgiou, Nikolaos S. ^{[1
]}

机构：

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 07期

关键词：

p-Laplacian; constant sign solutions; nodal solutions; concave-convex nonlinearity; second deformation theorem; upper-lower solution; truncated functional;

D O I：

10.1016/j.jde.2008.07.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlinear elliptic equation driven by the p-Laplacian with Dirichlet boundary conditions. Using variational techniques combined with the method of upper-lower solutions and suitable truncation arguments, we establish the existence of at least five nontrivial solutions. Two positive, two negative and a nodal (sign-changing) solution. Our framework of analysis incorporates both coercive and p-superlinear problems. Also the result on multiple constant sign solutions incorporates the case of concave-convex nonlinearities. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1883 / 1922

页数：40

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