Multiple and sign-changing solutions for the multivalued p-Laplacian equation

被引：9

作者：

Carl, Siegfried ^{[1
]}

Motreanu, Dumitru ^{[2
]}

机构：

[1] Univ Halle Wittenberg, Inst Math, D-06099 Halle, Germany

[2] Univ Perpignan, Dept Math, F-66860 Perpignan, France

来源：

MATHEMATISCHE NACHRICHTEN | 2010年 / 283卷 / 07期

关键词：

Sign-changing solution; p-Laplacian; elliptic inclusions; Clarke's generalized gradient; nonsmooth critical point theory; comparison principles; Fucik spectrum; INCLUSIONS; PRINCIPLE;

D O I：

10.1002/mana.200710049

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient. Under conditions given in terms of the rst eigenvalue as well as the Fucik spectrum of the p-Laplacian we prove the existence of a positive, a negative and a sign-changing solution. Our approach is based on variational methods for nonsmooth functionals (nonsmooth critical point theory, second deformation lemma), and comparison principles for multivalued elliptic problems. In particular, the existence of extremal constant-sign solutions plays a key role in the proof of sign-changing solutions. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：965 / 981

页数：17

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