Periodic Solutions for Second Order Equations with the Scalar p-Laplacian and Nonsmooth Potential

被引：1

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Yannakakis, Nikolaos ^{[1
]}

机构：

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

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2004年 / 47卷 / 01期

关键词：

Nonsmooth critical point theory; Locally Lipschitz function; Subdifferential; Linking sets; Linking theorem; Nonsmooth C-condition; p-Laplacian; Eigenvalues;

D O I：

10.1619/fesi.47.107

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we examine a scalar equation driven by the p-Laplacian and having periodic boundary conditions and a nonsmooth potential j(t, x). We assume that asymptotically at +/-infinity, the quantity pj(t,x)/vertical bar x vertical bar(p) lies between the first two eigenvalues lambda(0) = 0 and lambda(1), with possible interaction (resonance) with lambda(0) = 0. We show that the equation has a solution. The method of proof uses the nonsmooth Critical Point Theory and in particular a recently established version of the Linking Theorem.

引用

页码：107 / 117

页数：11

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