文献类型：期刊文献

英文题名：Ground state solutions andmultiple solutions for a p(x)-Laplacian equation in RN with periodic data

作者：Ji, Chao[1];Liao, Jie[1];Zhang, Binlin[2]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China;[2]Heilongjiang Inst Technol, Dept Math, Harbin, Peoples R China

年份：2017

卷号：62

期号：6

起止页码：825

外文期刊名：COMPLEX VARIABLES AND ELLIPTIC EQUATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000396930300008)】；

基金：The first author is Supported by NSFC [grant number 11301181]; China Postdoctoral Science Foundation, the second author is supported by Supported by NSFC [grant number 11301182]; Science and Technology Commission of Shanghai Municipality [grant number 13ZR1453400]; The third author is supported by Research Foundation of Heilongjiang Educational Committee [grant number 12541667].

语种：英文

外文关键词：p(x)-Laplacian equation; variable exponent Sobolev spaces; ground state solutions; multiplicity of solutions; Nehari manifold

摘要：In this work, we consider the following p(x)-Laplacian equation in R-N {- div(|Delta u|(p(x))-2(del u)) + V(x)|u| (p(x)-2)u = f (x, u), in R-N u is an element of W-1,W- p(x)(R-N), where f, V and p( x) are periodic in x(1), x(2),..., x(N). Under some appropriate assumptions, we prove the existence of the ground state solutions via the generalized Nehari method due to Szulkin and Weth. Moreover, if f is odd in u, infinitely many pairs of geometrically distinct solutions are given. To the best of our knowledge, our results are new even in the constant exponent case.