On nonlocal p(x)-Laplacian Dirichlet problems

被引：101
作者：
Fan, Xianling [1 ,2 ]
机构：
[1] Lanzhou City Univ, Dept Math, Lanzhou 730070, Peoples R China
[2] Lanzhou Univ, Dept Math, Lanzhou 730000, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 7-8期
基金：
中国国家自然科学基金;
关键词：
Kirchhoff equation; Nonlocal equation; p(x)-Laplacian; Variational method; ELLIPTIC-EQUATIONS; MULTIPLICITY RESULT; POSITIVE SOLUTIONS; VARIABLE EXPONENT; KIRCHHOFF-TYPE; SPACES; REGULARITY; EXISTENCE;
D O I：
10.1016/j.na.2009.12.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the nonlocal p(x)-Laplacian Dirichlet problems with non-variational form -A(u)Delta(p(x))u(x) = B(u)f(x, u(x)) in Omega; u vertical bar(partial derivative Omega) = 0, and with variational form -a(integral(Omega)vertical bar del u vertical bar(p(x))/p(x) dx) Delta(p(x))u(x) = b (integral F-Omega(x, u)dx) f(x, u (x)) in Omega; u vertical bar(partial derivative Omega) = 0, where F(x, t) = integral(t)(0) f(x, s)ds, and a is allowed to be singular at zero. Using (S+) mapping theory and the variational method, some results on existence and multiplicity for the problems are obtained under weaker hypotheses. Our results are also new even for the case when p(x) equivalent to p is a constant. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3314 / 3323
页数：10
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