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

Author

Dancer, E.N., Wei, Juncheng, and Weth, Tobias

Subjects
*A priori, *NONLINEAR difference equations, *ELLIPTIC coordinates, *ELLIPTIC operators, *BOSE-Einstein condensation, *MATHEMATICS education (Secondary)
Abstract

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 . [Copyright &y& Elsevier]

Published
2010
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