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

作　　者：葛斌 薛小平 周庆梅 

机构地区：[1]Department of Applied Mathematics, Harbin Engineering University [2]Department of Mathematics, Harbin Institute of Technology [3]Library, Northeast Forestry University

出　　处：《Acta Mathematica Scientia》2011年第5期1786-1802,共17页数学物理学报（B辑英文版）

基　　金：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.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：p（t）-Laplacian periodic solution variable exponent Sobolev space minimax principle generalized subdifferential local linking reduction method 

分 类 号：O175.7[理学—数学]