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Positive solution for asymptotically linear elliptic systems
Author(s) -
Peng Chaoquan,
Yang Jianfu
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1192
Subject(s) - mathematics , pure mathematics , mathematical analysis , discrete mathematics
In this paper, we show that semilinear elliptic systems of the form 1\documentclass{article}\footskip=0pc\usepackage{amssymb}\usepackage[mathscr]{euscript}\pagestyle{empty}\begin{document}\begin{eqnarray*}\left\{\begin{array}{ll}-(\Delta u-u)+\mathrm{\mu}(\Delta v-v)=g(x,v), & x \in {\mathbb{R}}^N\\-(\Delta v-v)+\lambda(\Delta u-u)=f(x,u), & x \in {\mathbb{R}}^N\end{array}\right.\end{eqnarray*}\end{document} possess at least one positive solution pair ( u, v )∈ H 1 (ℝ N )× H 1 (ℝ N ), where λ and µ are nonnegative numbers, f ( x, t ) and g ( x, t ) are continuous functions on ℝ N ×ℝ and asymptotically linear as t →+∞. Copyright © 2009 John Wiley & Sons, Ltd.