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

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.