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Ground states for scalar field equations with anisotropic nonlocal nonlinearities

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

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