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Ground state and non-ground state solutions of some strongly coupled elliptic systems

par Bonheure, Denis ;Moreira dos Santos, Ederson;Ramos, Miguel
Référence American Mathematical Society. Transactions, 364, 1, page (447-491)
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

We study an elliptic system of the form Lu = ⌊v⌋p&1 v and Lv = ⌊u⌋ q&1 u in Ω with homogeneous Dirichlet boundary condition, where Lu:= &Δu in the case of a bounded domain and Lu:= &Δu + u in the cases of an exterior domain or the whole space RN. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered. © 2011 American Mathematical Society.