Existence results for a Kirchhoff-type equation involving fractional p(x)-Laplacian

被引：4

作者：

Zhang, Jinguo ^{[1
]}

Yang, Dengyun ^{[1
]}

Wu, Yadong ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 08期

基金：

中国国家自然科学基金;

关键词：

fractional p(x)-Laplace operator; Kirchhoff-type equation; variational methods;

D O I：

10.3934/math.2021486

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to investigate the existence of weak solutions for a Kirchhoff type problem driven by a non-local integro-differential operator as follows: {M(integral R-2N) |u(x) - u(y)|(p(x,y))/p(x, y)|x -y|(N+sp(x,y)dxdy) ) (-Delta p(x))(s) u(x) = f(x, u) in Omega, u = 0 in RN\omega, where omega is a smooth bounded open set in R-N, s E (0, 1) and p is a positive continuous function with sp(x, y) < N, M and f are two continuous functions, (-Delta p(x))s is the fractional p(x)-Laplacian operator. Using variational methods combined with the theory of the generalized Lebesgue Sobolev space, we prove the existence of nontrivial solution for the problem in an appropriate space of functions.

引用

页码：8390 / 8403

页数：14

共 29 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] EIGENVALUE PROBLEMS INVOLVING THE FRACTIONAL p(x)-LAPLACIAN OPERATOR [J].