EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

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

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1786-1802.doi: 10.1016/S0252-9602(11)60361-5

EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

葛斌^*|薛小平|周庆梅

Department of Applied Mathematics, Harbin Engineering University, Harbin 150001, China； Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China； Library, Northeast Forestry University, Harbin 150040, China

收稿日期:2010-05-12 修回日期:2010-09-05 出版日期:2011-09-20 发布日期:2011-09-20
通讯作者: 葛斌，gebin04523080261@163.com E-mail:gebin04523080261@163.com；xiaopingxue@263.net；zhouqingmei2008@163.com
基金资助:
This work was supported by the National Science Foun-dation of China (11001063, 10971043), the Fundamental Research Funds for the Central Universities (HEUCF20111134), China Postdoctoral Science Foundation Funded Project (20110491032), Heilongjiang Provincial Sci-ence Foundation for Distinguished Young Scholars (JC200810), Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803).

EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

GE Bin^*, XUE Xiao-Ping, ZHOU Qiang-Mei

Department of Applied Mathematics, Harbin Engineering University, Harbin 150001, China； Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China； Library, Northeast Forestry University, Harbin 150040, China

Received:2010-05-12 Revised:2010-09-05 Online:2011-09-20 Published:2011-09-20
Contact: GE Bin，gebin04523080261@163.com E-mail:gebin04523080261@163.com；xiaopingxue@263.net；zhouqingmei2008@163.com
Supported by:
This work was supported by the National Science Foun-dation of China (11001063, 10971043), the Fundamental Research Funds for the Central Universities (HEUCF20111134), China Postdoctoral Science Foundation Funded Project (20110491032), Heilongjiang Provincial Sci-ence Foundation for Distinguished Young Scholars (JC200810), Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803).

摘要/Abstract

摘要：

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

关键词: p(t)-Laplacian, periodic solution, variable exponent Sobolev space, minimax principle, generalized subdifferential, local linking reduction method

Key words: p(t)-Laplacian, periodic solution, variable exponent Sobolev space, minimax principle, generalized subdifferential, local linking reduction method

中图分类号:

34C25

葛斌, 薛小平, 周庆梅. EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN[J]. 数学物理学报(英文版), 2011, 31(5): 1786-1802.

GE Bin, XUE Xiao-Ping, ZHOU Qiang-Mei. EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1786-1802.

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EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

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