含有Hardy-Sobolev临界指标的奇异拟线性椭圆系统在无界外区域的无穷多解

Infinitely Many Solutions for Singular Quasilinear Elliptic Systems Involving the Critical Hardy-Sobolev Exponents on an Unbounded Exterior Domain

文中研究一类奇异p-Laplacian方程组在无界域上解的存在性。方程组中的非线性项含有Hardy-Sobolev临界指标项。利用变分方法,证明了这类问题解存在无穷多个解。

In this paper,we study a class of singular quasilinear elliptic systems involving the p-Laplacian operator on an unbounded exterior domain.The right-hand sides of systems are closely related to the critical Hardy-Sobolev exponents.Under some additional assumptions on the nonlinearities,we use the variational methods to prove the existence of infinitely many solutions.