Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems

Title:

Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems

Creator:

Papageorgiou, Evgenia H. and Papageorgiou, Nikolaos S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6260bc36-c715-4ea0-a9cb-bb86f5bf41e1
uuid:6260bc36-c715-4ea0-a9cb-bb86f5bf41e1

Subject:

$p$-Laplacian, nonsmooth critical point theory, Clarke subdifferential, saddle point theorem, periodic solution, Poincare-Wirtinger inequality, Sobolev inequality, and nonsmooth Palais-Smale condition

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we examine nonlinear periodic systems driven by the vectorial $p$-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. $p = 2$) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the “superlinear” problem. Our work generalizes some recent results of Tang (PAMS 126(1998)).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

347-371

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:2

Harvested from:

CDK

Metadata only:

false