Existence of at least five solutions for a differential inclusion problem involving the p(x)-Laplacian

Bin Ge; Xiaoping Xue; Qingmei Zhou

doi:10.1016/j.nonrwa.2011.01.011

Existence of at least five solutions for a differential inclusion problem involving the p(x)-Laplacian

Bin Ge^*
, Xiaoping Xue
, Qingmei Zhou

^*Corresponding author for this work

School of Mathematics

Harbin Engineering University
Harbin Institute of Technology
Northeast Forestry University

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

13 Scopus citations

Abstract

We studied a nonlinear Dirichlet problem driven by the p(x)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method combined with suitable truncation techniques based on nonsmooth critical point theory for locally Lipschitz function, we proved the existence of at least five solutions under the suitable conditions.

Original language	English
Pages (from-to)	2304-2318
Number of pages	15
Journal	Nonlinear Analysis: Real World Applications
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/j.nonrwa.2011.01.011
State	Published - Aug 2011

Keywords

Dirichlet problem
Elliptic equation
Generalized subdifferential
Variable exponent Sobolev space
p(x)-Laplacian

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10.1016/j.nonrwa.2011.01.011

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title = "Existence of at least five solutions for a differential inclusion problem involving the p(x)-Laplacian",

abstract = "We studied a nonlinear Dirichlet problem driven by the p(x)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method combined with suitable truncation techniques based on nonsmooth critical point theory for locally Lipschitz function, we proved the existence of at least five solutions under the suitable conditions.",

keywords = "Dirichlet problem, Elliptic equation, Generalized subdifferential, Variable exponent Sobolev space, p(x)-Laplacian",

author = "Bin Ge and Xiaoping Xue and Qingmei Zhou",

year = "2011",

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T1 - Existence of at least five solutions for a differential inclusion problem involving the p(x)-Laplacian

AU - Ge, Bin

AU - Xue, Xiaoping

AU - Zhou, Qingmei

PY - 2011/8

Y1 - 2011/8

N2 - We studied a nonlinear Dirichlet problem driven by the p(x)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method combined with suitable truncation techniques based on nonsmooth critical point theory for locally Lipschitz function, we proved the existence of at least five solutions under the suitable conditions.

AB - We studied a nonlinear Dirichlet problem driven by the p(x)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method combined with suitable truncation techniques based on nonsmooth critical point theory for locally Lipschitz function, we proved the existence of at least five solutions under the suitable conditions.

KW - Dirichlet problem

KW - Elliptic equation

KW - Generalized subdifferential

KW - Variable exponent Sobolev space

KW - p(x)-Laplacian

UR - https://www.scopus.com/pages/publications/79955524450

U2 - 10.1016/j.nonrwa.2011.01.011

DO - 10.1016/j.nonrwa.2011.01.011

M3 - 文章

AN - SCOPUS:79955524450

SN - 1468-1218

VL - 12

SP - 2304

EP - 2318

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 4

ER -

Existence of at least five solutions for a differential inclusion problem involving the p(x)-Laplacian

Abstract

Keywords

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