Nonlinear scalar field equations: Existence of a positive solution with infinitely many bumps
Giovanna Cerami
Politecnico di Bari, Dipartimento di Meccanica, Matematica e Management, Via Orabona 4, 70125 Bari, ItalyDonato Passaseo
Università del Salento, Dipartimento di Matematica e Fisica, Ex Collegio Fiorini, Via per Arnesano, 73047 Monteroni di Lecce (LE), ItalySergio Solimini
Politecnico di Bari, Dipartimento di Meccanica, Matematica e Management, Via Orabona 4, 70125 Bari, Italy
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Abstract
In this paper we consider the equation
where , , , if . During last thirty years the question of the existence and multiplicity of solutions to () has been widely investigated mostly under symmetry assumptions on . The aim of this paper is to show that, differently from those found under symmetry assumption, the solutions found in [6] admit a limit configuration and so () also admits a positive solution of infinite energy having infinitely many ‘bumps’.
Résumé
Dans ce papier nous considérons l'équation
où , , , si . Pendant les trente dernières années la question de l'existence et de la multiplicité de solutions d‘ () a été largement examinée surtout conformément aux suppositions de symétrie sur . Le but de ce papier est de montrer que, différemment de ceux trouvés conformément à la supposition de symétrie, les solutions trouvées dans [6] admettent une configuration de limite et donc () admet aussi une solution positive d'énergie infinie ayant une infinité de ‘bumps’.
Cite this article
Giovanna Cerami, Donato Passaseo, Sergio Solimini, Nonlinear scalar field equations: Existence of a positive solution with infinitely many bumps. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 23–40
DOI 10.1016/J.ANIHPC.2013.08.008