Ground states for scalar field equations with anisotropic nonlocal nonlinearities | Zendy

Antonio Iannizzotto | Zendy; Kanishka Perera | Zendy; Marco Squassina | Zendy

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Ground states for scalar field equations with anisotropic nonlocal nonlinearities

Author(s) -

Antonio Iannizzotto,

Kanishka Perera,

Marco Squassina

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.5963

Subject(s) - compact space , scalar field , ground state , anisotropy , scalar (mathematics) , lemma (botany) , infinity , physics , limit (mathematics) , mathematical physics , exponent , mathematics , mathematical analysis , quantum mechanics , ecology , linguistics , philosophy , geometry , poaceae , biology

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

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