Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition  

作　　者：Zifei SHEN Chenyin QIAN 

机构地区：[1]College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

出　　处：《Chinese Annals of Mathematics,Series B》2009年第4期397-412,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10771141);the ZhejiangProvincial Natural Science Foundation of China (No. Y7080008).

摘　　要：The authors study the p(x)-Laplacian equations with nonlinear boundary condi- tion. By using the variational method, under appropriate assumptions on the perturbation terms f1(x,u), f2(x,u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.

关 键 词：p（x）-Laplacian Nonlinear boundary condition （PS） condition Mountain pass lemma Fountain theorem 

分 类 号：O175.26[理学—数学] O175.25[理学—基础数学]