Ground states for scalar field equations with anisotropic nonlocal nonlinearities

Antonio  Iannizzotto; Kanishka Perera; Marco Squassina

doi:10.3934/dcds.2015.35.5963

Article Contents

2015, Volume 35, Issue 12: 5963-5976. Doi: 10.3934/dcds.2015.35.5963

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Ground states for scalar field equations with anisotropic nonlocal nonlinearities

1.
Department of Mathematics and Computer Science, University of Cagliari, Viale L. Merello 92, 09123 Cagliari
2.
Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901
3.
Dipartimento di Informatica, Università di Verona, Strada Le Grazie 15, 37134 Verona

Received: December 31, 2013

Published: November 2015

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Abstract

We consider a class of scalar field equations with anisotropic nonlocal nonlinearities. We obtain a suitable extension of the well-known compactness lemma of Benci and Cerami to this variable exponent setting, and use it to prove that the Palais-Smale condition holds at all level below a certain threshold. We deduce the existence of a ground state when the variable exponent slowly approaches the limit at infinity from below.

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Mathematics Subject Classification: Primary: 35J20, 46B50; Secondary: 74G65.

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