A note on a superlinear and periodic elliptic system in the whole space

Shuying He; Rumei Zhang; Fukun Zhao

doi:10.3934/cpaa.2011.10.1149

Article Contents

2011, Volume 10, Issue 4: 1149-1163. Doi: 10.3934/cpaa.2011.10.1149

This issue Previous Article A continuum of extinction rates for the fast diffusion equation Next Article The inverse Fueter mapping theorem

A note on a superlinear and periodic elliptic system in the whole space

1.
Department of Mathematics, Yunnan Normal University, Kunming 650092 Yunnanage
2.
Office of Adult Education, Simao Teacher's College, Simao 665000 Yunnan
3.
Department of Mathematics, Yunnan Normal University, Kunming 650092 Yunnan

Received: April 2010

Revised: December 2010

Published: July 2011

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Abstract

This paper is concerned with the following periodic Hamiltonian elliptic system

$ -\Delta u+V(x)u=g(x,v)$ in $R^N,$

$ -\Delta v+V(x)v=f(x,u)$ in $R^N,$

$ u(x)\to 0$ and $v(x)\to 0$ as $|x|\to\infty,$

where the potential $V$ is periodic and has a positive bound from below, $f(x,t)$ and $g(x,t)$ are periodic in $x$ and superlinear but subcritical in $t$ at infinity. By using generalized Nehari manifold method, existence of a positive ground state solution as well as multiple solutions for odd $f$ and $g$ are obtained.

Keywords:

Mathematics Subject Classification: Primary: 35J50; Secondary: 35J55.

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References

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