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

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 u...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 8; no. 1; pp. 1184 - 1212
Main Authors Cassani, Daniele, Zhang, Jianjun
Format Journal Article
LanguageEnglish
Published De Gruyter 01.01.2019
Subjects
35B25
35B33
35J61
Choquard equation
Ground states
Hardy–Littlewood–Sobolev inequality
semiclassical states
upper-critical exponent
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Summary: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.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2018-0019