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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
- Source :
- Advances in Nonlinear Analysis, Vol 8, Iss 1, Pp 1184-1212 (2018)
- Publication Year :
- 2018
- Publisher :
- De Gruyter, 2018.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 21919496 and 2191950X
- Volume :
- 8
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Advances in Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.8d822445077443c69349d777f36d6589
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/anona-2018-0019