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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:245

Article

Filippakis, Michael E.¹  Papageorgiou, Nikolaos S.¹ 

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

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

DOI  :  10.1016/j.jde.2008.07.004

来源: Elsevier

【 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.

【 授权许可】

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