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EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN
引用本文: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(B辑英文版),2011,31(5):1786-1802.
作者姓名:葛斌  薛小平  周庆梅
作者单位:Department of Applied Mathematics;Harbin Engineering University;Department of Mathematics;Harbin Institute of Technology;Library;Northeast Forestry University;
基金项目:supported by the National Science Foundation of China (11001063, 10971043); the Fundamental Research Funds for the Central Universities (HEUCF 20111134); China Postdoctoral Science Foundation Funded Project (20110491032); Heilongjiang Provincial Science 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: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.

关 键 词:Laplacian  差分系统  周期解  Laplace算子  非平凡解  临界点理论  问题驱动  变分方法
收稿时间:12 May 2010

Existence of periodic solutions for a differential inclusion systems involving the p(t)-Laplacian
Ge Bin,Xue Xiaoping,Zhou Qingmei.Existence of periodic solutions for a differential inclusion systems involving the p(t)-Laplacian[J].Acta Mathematica Scientia,2011,31(5):1786-1802.
Authors:Ge Bin  Xue Xiaoping  Zhou Qingmei
Institution:aDepartment of Applied Mathematics, Harbin Engineering University, Harbin 150001, China;bDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, China;cLibrary, Northeast Forestry University, Harbin 150040, China
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.
Keywords:p(t)-Laplacian  periodic solution  variable exponent Sobolev space  minimax principle  generalized subdifferential  local linking reduction method
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