Multi-bump type nodal solutions having a prescribed number of nodal domains: II

Abstract

This paper is a sequel to [Liu and Wang, preprint] in which we studied nodal property of multi-bump type sign-changing solutions constructed by Coti Zelati and Rabinowitz [Comm. Pure Appl. Math. 45 (1992) 1217]. In this paper we remove a technical condition that the nonlinearity is odd, which was used in [Comm. Pure Appl. Math. 45 (1992) 1217; Liu and Wang, Multi-bump type nodal solutions having a prescribed number of nodal domains: I, Ann. I. H. Poincaré – AN 22 (2005) 597–608] for constructing multi-bump type nodal solutions having a prescribed number of nodal domains.

Résumé

Cet article est la suite de [Liu and Wang, preprint] sur l'analyse de la propriété nodale des solutions des multi-bosses, construites par Coti Zelati et Rabinowitz dans [Comm. Pure Appl. Math. 45 (1992) 1217]. Nous supprimons la condition technique que le terme nonlinéaire impair comme elle est utilisée dans [Comm. Pure Appl. Math. 45 (1992) 1217; Liu and Wang, Multi-bump type nodal solutions having a prescribed number of nodal domains: I, Ann. I. H. Poincaré – AN 22 (2005) 597–608], pour construire des solutions nodales de multi-bosses ayant un nombre de domaines nodaux prescrits.