Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in

  • Otared Kavian

    Université de Versailles, Département de Mathématiques, 45, avenue des États-Unis, 78035 Versailles Cedex, France
  • Khalid Benmlih

    Université de Fès, Département des Sciences Economiques, BP 42 A, 30000 Fès, Maroc

Abstract

In this work we are concerned with existence and asymptotic behaviour of standing wave solutions in the whole space for the quasilinear Schrödinger–Poisson system

when the nonlinearity coefficient goes to zero. Under appropriate, almost optimal, assumptions on the potential and the density we establish existence of a ground state of the above system, for all ɛ sufficiently small, and show that converges to , the ground state solution of the corresponding system for .

Cite this article

Otared Kavian, Khalid Benmlih, Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in . Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 3, pp. 449–470

DOI 10.1016/J.ANIHPC.2007.02.002