Positive solutions and multiple solutions for periodic problems driven by scalar p-Laplacian

被引：7
|
作者：
Hu, Shouchuan
Papageorgiou, N. S.
机构：
[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
[2] SW Missouri State Univ, Dept Math, Springfield, MO 65804 USA
来源：
MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 12期
关键词：
nonsmooth critical point theory; locally Lipschitz function; generalized subdifferential; nonsmooth PS-condition; Mountain Pass Theorem; positive solution; multiple solutions;
D O I：
10.1002/mana.200310423
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study a nonlinear second order periodic problem driven by a scalar p-Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
引用
收藏
页码：1321 / 1334
页数：14
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