1. Academy of Mathematics and System Science, Academia Sinica, Beijing 100080, PR China;2. Department of Mathematics, Yunnan Normal University, Kunming 650092, PR China
Abstract:
In this paper we establish the existence of a positive solution of the Schrödinger–Poisson equations with a critical Sobolev exponent. The methods used here are based on the concentration–compactness principle of P. L. Lions and methods of Brezis and Nirenberg.