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.

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

Cassani, Daniele
;
Zhang, Jianjun
2018-01-01

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.
http://www.degruyter.com/view/j/anona?rskey=nXQd01&result=2
Choquard equation; Ground states; Hardy-Littlewood-Sobolev inequality; semiclassical states; upper-critical exponent; Analysis
Cassani, Daniele; Zhang, Jianjun
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2077837
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