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A note on solutions for asymptotically linear elliptic systems

A note on solutions for asymptotically linear elliptic systems In this paper, we are concerned with the elliptic system of $$ \left\{ {\begin{array}{*{20}c} { - \Delta u + V(x)u = g(x,v), x \in R^N ,} \\ { - \Delta v + V(x)v = f(x,u), x \in R^N ,} \\ \end{array} } \right. $$ where V (x) is a continuous potential well, ƒ, g are continuous and asymptotically linear as t → ∞. The existence of a positive solution and ground state solution are established via variational methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A note on solutions for asymptotically linear elliptic systems

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-008-8043-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we are concerned with the elliptic system of $$ \left\{ {\begin{array}{*{20}c} { - \Delta u + V(x)u = g(x,v), x \in R^N ,} \\ { - \Delta v + V(x)v = f(x,u), x \in R^N ,} \\ \end{array} } \right. $$ where V (x) is a continuous potential well, ƒ, g are continuous and asymptotically linear as t → ∞. The existence of a positive solution and ground state solution are established via variational methods.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Aug 6, 2008

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