含Sobolev-Hardy临界指数的p-Laplace方程组正解的存在性

Existence of Positive Solutions for a Class of p-Laplacian Systems Involving Critical Sobolev-Hardy Exponents

研究了一类含Sobolev-Hardy临界指数的p-Laplace方程组,首先利用达到函数找到了能量泛函在Nehari流形上的鞍点,然后运用集中紧原理解决了紧性问题,从而得到了方程组正解的存在性,丰富和改进了现有的结果.

In this paper,we consider a class of p-Laplacian systems involving critical Sobolev-Hardy exponents.Firstly,by using extremal function,the saddle of energy functional on Nehari manifold is located.Then we exploit concentration compactness principle to solve the problem of compactness and obtain the existence of positive solutions.Consequently,the current result is generalized.