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. 953–969DOI 10.1016/J.ANIHPC.2010.01.009