一类带有变指数增长的Neumann问题  

A Class of Neumann Problems with Variable Exponential Growth

作　　者：蒙璐 储昌木 雷俊 MENG Lu;CHU Chang-mu;LEI Jun(College of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《西南大学学报（自然科学版）》2021年第6期82-88,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861021).

摘　　要：考虑一类带有变号位势和变指数的半线性Neumann边值问题,通过空间分解技术和变号位势函数的一些性质,证明了该类问题的泛函满足(PS)条件且具有山路几何结构,利用变分方法获得了该类问题两个非平凡解的存在性.In this paper,we consider a class of semilinear Neumann boundary value problems with variable sign potential function and variable exponent.Using the space decomposition technique and some properties of sign-changing potential function,we prove that the functional of such problems satisfies the(PS)conditions and has astructure of mountain pass geometry.With the variational method,we obtain the existence of two nontrivial solutions of these problems.

关 键 词：NEUMANN边值问题 变指数增长 变号位势 变分方法 

分 类 号：O175.25[理学—数学]