Existence of periodic solutions for a differential inclusion systems involving the p(t)-Laplacian

Ge Bin; Xue Xiaoping; Zhou Qingmei

doi:10.1016/S0252-9602(11)60361-5

Existence of periodic solutions for a differential inclusion systems involving the p(t)-Laplacian

Ge Bin^*
, Xue Xiaoping
, Zhou Qingmei

^*Corresponding author for this work

School of Mathematics

Harbin Engineering University
Northeast Forestry University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.

Original language	English
Pages (from-to)	1786-1802
Number of pages	17
Journal	Acta Mathematica Scientia
Volume	31
Issue number	5
DOIs	https://doi.org/10.1016/S0252-9602(11)60361-5
State	Published - Sep 2011

Keywords

Generalized subdifferential
Local linking reduction method
Minimax principle
P(t)-Laplacian
Periodic solution
Variable exponent Sobolev space

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10.1016/S0252-9602(11)60361-5

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abstract = "We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.",

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AU - Xiaoping, Xue

AU - Qingmei, Zhou

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N2 - We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.

AB - We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.

KW - Generalized subdifferential

KW - Local linking reduction method

KW - Minimax principle

KW - P(t)-Laplacian

KW - Periodic solution

KW - Variable exponent Sobolev space

UR - https://www.scopus.com/pages/publications/79961174316

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JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 5

ER -

Existence of periodic solutions for a differential inclusion systems involving the p(t)-Laplacian

Abstract

Keywords

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