Nehari's problem and competing species systems
M. Conti
Dipartimento di Matematica, Politecnico di Milano, P.zza L. da Vinci, 32, 20133 Milano (I), ItalyS. Terracini
Dipartimento di Matematica, Politecnico di Milano, P.zza L. da Vinci, 32, 20133 Milano (I), ItalyG. Verzini
Dipartimento di Matematica, Politecnico di Milano, P.zza L. da Vinci, 32, 20133 Milano (I), Italy
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Abstract
We consider an optimal partition problem in N-dimensional domains related to a method introduced by Nehari [22]. We prove existence of the minimal partition and some extremality conditions. Moreover we show some connections between the variational problem, the behaviour of competing species systems with large interaction and changing sign solutions to elliptic superlinear equations.
Résumé
Nous étudions un problème de partition optimale dans qui se relie à une métode introduite par Nehari [22]. Nous établissons l’existence de la partition optimale et quelques conditions d’extremalité. En plus nous démontrons un lien entre le problème variationel, le comportement asymptotique de certains systèmes quand l’interaction tends à l’infini et les solutions qui changent de signe pour les equations elliptiques surlinéaires.
Cite this article
M. Conti, S. Terracini, G. Verzini, Nehari's problem and competing species systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002), no. 6, pp. 871–888
DOI 10.1016/S0294-1449(02)00104-X