Ground State Solutions for a Class of Choquard Equations Involving Doubly Critical Exponents  

作　　者：Yong-yong LI Gui-dong LI Chun-lei TANG 

机构地区：[1]School of Mathematics and Statistics,Southwest University,Chongqing,400715,China [2]College of Mathematics and Statistics,Northwest Normal University,Lanzhou,730070,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第4期820-840,共21页应用数学学报（英文版）

基　　金：This paper is supported by the National Natural Science Foundation of China(No.11971393).

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.

关 键 词：choquard equation doubly critical exponents ground state solution 

分 类 号：O175[理学—数学]