Ground states for scalar field equations with anisotropic nonlocal nonlinearities

IANNIZZOTTO, ANTONIO;Perera K;Squassina M.

2015-01-01

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Abstract

We consider a class of scalar field equations with anisotropic non-local 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.