含Hardy-Sobolev临界指数项的p-q型椭圆边值问题的非平凡解

On Nontrivial Solutions of p-q Laplacian Type Elliptic Boundary Value Problems Involving Hardy-Sobolev Critical Exponents

讨论一类含有Hardy-Sobolev临界指数项的p-q型椭圆方程.由变分方法及山路引理,得到方程正解的存在性,应用Lyusternik-Schnirelman指标理论,得到方程的无穷多解.

This paper is dedicated to studying a class of p-q Laplacian elliptic equations with Hardy-Sobolev critical exponents. We obtain a positive solution by using the variational methods and the mountain pass theorem. And based upon the Lyusternik-Schnirelman index theory, we also prove that there exist infinitely many weak solutions.