Ground states for scalar field equations with anisotropic nonlocal nonlinearities

2014/01/17 by Iannizzotto, Antonio, Perera, Kanishka, Squassina, Marco
#35J20 #46B50 #74G65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.4487

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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