一类带有变指数算子的非局部问题解的存在性

Existence of Solutions for a Nonlocal Problem with Variable Exponent Operator

中文关键词:  变分方法  非局部问题  临界点理论  类~$(p(x),q(x))$-拉普拉斯算子  弱解

英文关键词:variational methods  nonlocal problem  critical point theory  $(p(x),q(x))$-Laplacian-like operator  weak solutions

中文摘要:

      研究源于毛细现象的一类带有类$(p(x),q(x))$-拉普拉斯算子的非局部狄利克雷问题. 利用变分方法和临界点理论, 得到了此问题无穷多个弱解的存在性.

英文摘要:

      The purpose of this paper is to investigate a nonlocal Dirichlet problem with $(p(x),q(x))$-Laplacian-like operator originated from a capillary phenomena. Using the variational methods and the critical point theory, we establish the existence of infinitely many weak solutions for this problem.