带类p(x)-拉普拉斯算子的双非局部问题的无穷多解  

Infinitely Many Solutions for a Bi-Nonlocal Problem Involving p(x)-Laplacian-Like Operator

作　　者：张申贵[1] Zhang Shengui(School of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 73003)

机构地区：[1]西北民族大学数学与计算机科学学院,兰州730030

出　　处：《数学物理学报（A辑）》2018年第3期514-526,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(31260098);甘肃省科技计划项目(1610RJZA102);中央高校基本科研业务专项经费(31920170147)~~

摘　　要：该文运用变分方法研究一类带类P(x)-拉普拉斯算子的双非局部狄利克雷问题.利用喷泉定理和对称山路定理,得到了此类问题一列高能量和低能量解的存在性.In this article, we study a class of bi-nonlocal Dirichlet problem involving p（x）-Laplacian-like operator via variational methods. Using the fountain theorem and the symmetric mountain pass theorem, the existence of a sequence of high and low energy solutions for this problem are obtained, respectively.

关 键 词：变分方法 临界点 类p(x)-拉普拉斯算子 非局部问题 弱解 

分 类 号：O177.91[理学—数学]