Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

Advances in Nonlinear Analysis

article

Daniele Cassani¹  Jianjun Zhang³ 

[1] Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria;RISM–Riemann International School of Mathematics;College of Mathematics and Statistics, Chongqing Jiaotong University

关键词: Ground states;    semiclassical states;    Choquard equation;    Hardy–Littlewood–Sobolev inequality;    upper-critical exponent;   

DOI  :  10.1515/anona-2018-0019

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood–Sobolev inequality, in the range of the so-called upper-critical exponent. Qualitative behavior and concentration phenomena of solutions are also studied. Our approach turns out to be robust, as we do not require the nonlinearity to enjoy monotonicity nor Ambrosetti–Rabinowitz-type conditions, still using variational methods.

【 授权许可】

CC BY