Infinitely Many Solutions for a Non-homogeneous Differential Inclusion with Lack of Compactness

被引：9

作者：

Ge, Bin ^{[3
]}

Radulescu, Vicentiu D. ^{[1
,2
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[2] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest 014700, Romania

[3] Harbin Engn Univ, Sch Math Sci, Harbin 150001, Heilongjiang, Peoples R China

来源：

ADVANCED NONLINEAR STUDIES | 2019年 / 19卷 / 03期

基金：

中国国家自然科学基金;

关键词：

p(x)-Laplacian; Differential Inclusion Problem; Locally Lipschitz Function; Infinitely many Solutions; Variational Method; CRITICAL-POINTS; FUNCTIONALS; P(X)-LAPLACIAN; THEOREMS;

D O I：

10.1515/ans-2019-2047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following class of differential inclusion problems in R-N involving the p(x)-Laplacian: -Delta(p(x))u + V(x)vertical bar u vertical bar(p(x)-2)u is an element of a(x)partial derivative F(x, u) in R-N. We are concerned with a multiplicity property, and our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the nonsmooth symmetric mountain pass lemma and the fountain theorem, we establish conditions such that the associated energy functional possesses infinitely many critical points, and then we obtain infinitely many solutions.

引用

页码：625 / 637

页数：13

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