期刊
ADVANCES IN NONLINEAR ANALYSIS
卷 8, 期 1, 页码 1184-1212出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2018-0019
关键词
Ground states; semiclassical states; Choquard equation; Hardy-Littlewood-Sobolev inequality; upper-critical exponent
We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrodinger 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.
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