摘要
In this paper,we are concerned with the autonomous Choquard equation−Δu+u=(Iα∗|u|^(α/N+1))|u|^(α/N−1)u+|u|^(2∗−2)u+f(u)inR^(N),where N≥3,Iαdenotes the Riesz potential of orderα∈(0,N),the exponentsα/N+1 and 2^(∗)=2N/(N−2)are critical with respect to the Hardy-Littlewood-Sobolev inequality and Sobolev embedding,respectively.Based on the variational methods,by using the minimax principles and the Pohožaev manifold method,we prove the existence of ground state solution under some suitable assumptions on the perturbation f.
基金
This paper is supported by the National Natural Science Foundation of China(No.11971393).
