期刊论文

Two Solutions for Quasilinear Elliptic Equation with Hardy Potential on RN

中文

数学物理学报

1003-3998

2018

38

6

1153-1161

10.3969/j.issn.1003-3998.2018.06.012

国家自然科学基金（11371159）~~；

本校为第一机构

该文主要运用变分方法研究如下拟线性椭圆方程$$ - \sum\limits_{i = 1}^N {\frac{\partial }{{\partial {x_i}}}\left( {{{\left| {\nabla u} \right|}^{p - 2}}\frac{{\partial u}}{{\partial {x_i}}}} \right)} - \mu \frac{{{{\left| u \right|}^{p - 2}}u}}{{{{\left| x \right|}^p}}} = {\left| u \right|^{p* - 2}}u + \lambda g\left( x \right)u \in {D^{1,p}}\left( {{\mathbb{R}^N}} \right),$$在一定条件下两个非平凡解的存在性.其中一个解是通过局部极小得到的,另一个是运用山路引理得到的.

In the paper, we used variational method to consider the following quasilinear elliptic equation $$ - \sum\limits_{i = 1}^N {\frac{\partial }{{\partial {x_i}}}\left( {{{\left| {\nabla u} \right|}^{p - 2}}\frac{{\partial u}}{{\partial {x_i}}}} \right)} - \mu \frac{{{{\left| u \right|}^{p - 2}}u}}{{{{\left| x \right|}^p}}} = {\left| u \right|^{p* - 2}}u + \lambda g\left( x \right)u \in {D^{1,p}}\left( {{\mathbb{R}^N}} \right),$$ we show that there exists two nontrivial solutions for our problem, one solutio...