一类拟线性椭圆方程解的存在性  

The Existence of Solutions for a Class of Quasilinear Elliptic Equations

作　　者：高芳 陈林[1] GAO Fang;CHEN Lin(School of Mathematics and Statistics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范学院数学与统计分院

出　　处：《安徽师范大学学报（自然科学版）》2019年第4期317-321,共5页Journal of Anhui Normal University(Natural Science)

基　　金：新疆维吾尔自治区自然科学基金(2017D01C420)

摘　　要：本文研究一类拟线性椭圆问题-div(|x|^-ap|■u|^p-2■u)+V(x)|u|^p-2u=f(u,|■u|^p-2■u),其中x∈R^N,1<p<N,V(x)∈C(R^N),当|x|→+∞时,V(x)→+∞,f是非线性的且含有解的梯度项利用基于山路技巧的迭代方法得到问题正解的存在性。In this paper,we consider the quasilinear elliptic equation:-div(|x|^-ap|■u|^p-2■u)+V(x)|u|^p-2u=f(u,|■u|^p-2■u) in R^N,where 1<p<N and f is a nonlinearity depending also on the gradient of the solution.The existence of a positive solution is stated through an iterative method based on Mountain Pass techniques.

关 键 词：椭圆方程 山路定理 变分方法 迭代方法 

分 类 号：O175[理学—数学]