Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions

Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions

In this article, we study a periodic second-order differential inclusions with locally Lipschitz potentials. By means of the least action principle and the minimax principle of nonsmooth type, we prove the existence of two nontrivial periodic solutions under the weak AR-conditions. The method d...

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Bibliographic Details
Main Authors: Lizhen Chen, Qinghua Zhang, Gang Li
Format: Article
Language:English
Published: Texas State University 2014-06-01
Series:Electronic Journal of Differential Equations
Subjects:
Sobolev space
periodic solution
locally Lipschitz potential
AR-condition
nonsmooth C-condition
the least action principle
mountain pass lemma
Online Access:http://ejde.math.txstate.edu/Volumes/2014/136/abstr.html
Description
Summary:In this article, we study a periodic second-order differential inclusions with locally Lipschitz potentials. By means of the least action principle and the minimax principle of nonsmooth type, we prove the existence of two nontrivial periodic solutions under the weak AR-conditions. The method developed in this paper can be applied for studying second-order differential inclusions of periodic type, and for elliptic equations with Neumann boundary condition.
ISSN:1072-6691

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