A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system

  • Tobias Weth

    Mathematische Institut, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany
  • E.N. Dancer

    School of Mathematics and Statistics, University of Sydney, Australia
  • Juncheng Wei

    Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong

Abstract

We study the set of solutions of the nonlinear elliptic system

in a smooth bounded domain , , with coupling parameter . This system arises in the study of Bose–Einstein double condensates. We show that the value is critical for the existence of a priori bounds for solutions of (P). More precisely, we show that for , solutions of (P) are a priori bounded. In contrast, when , , (P) admits an unbounded sequence of solutions if .

Cite this article

Tobias Weth, E.N. Dancer, Juncheng Wei, A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 3, pp. 953–969

DOI 10.1016/J.ANIHPC.2010.01.009