p(x)-Laplacian Neumann问题的解与多解(英文)  

Solution and Multiple Solutions for p(x)-Laplacian Neumann Problem

作　　者：周美秀[1] 潜陈印[2] 蒋忠樟[3] 

机构地区：[1]浙江长征职业技术学院基础部,杭州浙江310023 [2]浙江师范大学数理与信息工程学院,金华浙江321004 [3]金华职业技术学院,金华浙江321017

出　　处：《数学进展》2010年第3期361-374,共14页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10971194);Natural Science Foundation of Zhejiang Province(No.Y7080008)

摘　　要：本文在W^(1,p(x))(Ω)上讨论了位势非光滑且只是局部Lipschitz的p(x)-LaplacianNeumann问题,利用极小极大原理和局部环绕定理获得了Neumann问题的存在性和多解性结果.In this paper we study the Neumann problem of p（x）-Laplacian with nonsmooth potential which is only locally Lipschitz.By the theory of minimax principle,we prove the existence result and through the local linking theorem we obtain multiplicity results for the following Neumann problem.The discussion is based on the theory of W^（1,p（x））（Ω）.

关 键 词：p(x)-Laplacian NEUMANN问题 局部环绕条件 局部Lipschitz泛函 

分 类 号：O177.92[理学—数学]