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Asymptotic behaviour of ground states

Authors: Josephus Hulshof and Robertus C. A. M. van der Vorst
Journal: Proc. Amer. Math. Soc. 124 (1996), 2423-2431
MSC (1991): Primary 35J55; Secondary 34C37
MathSciNet review: 1363170
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Abstract: We derive the asymptotic behaviour of the ground states of a system of two coupled semilinear Poisson equations with a strongly indefinite variational structure in the critical Sobolev growth case.

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Additional Information

Josephus Hulshof
Affiliation: Mathematical Department of the Leiden University, Niels Bohrweg 1 2333 CA Leiden, The Netherlands

Robertus C. A. M. van der Vorst
Affiliation: Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30308-0190

Keywords: Systems, strongly indefinite variational structure, critical Sobolev growth, ground states, asymptotic behaviour, transformation to $3$- and $4$-dimensional quadratic systems, heteroclinic orbits, critical point analysis.
Received by editor(s): February 16, 1995
Additional Notes: We gratefully acknowledge the support by N.W.O., the Dutch Organisation for Scientific Research, and Enzo Mitidieri for his encouragement.
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1996 American Mathematical Society

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