July  2009, 23(3): 1073-1086. doi: 10.3934/dcds.2009.23.1073

On a diffusion system with bounded potential

1. 

Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100080

2. 

Department of Mathematics, Yunnan Normal University, Kunming 650092 Yunnan, China

Received  February 2008 Revised  August 2008 Published  November 2008

This paper is concerned with the following non-periodic diffusion system

$\partial_tu-\Delta_x u+b(t,x)\cdot\nabla_x u+V(x)u=H_v(t,x,u,v)$in $\mathbb{R}\times\mathbb{R}^N,$ $-\partial_tv-\Delta_x v-b(t,x)\cdot\nabla_x v+V(x)v=H_u(t,x,u,v)$in$\mathbb{R}\times\mathbb{R}^N,$
$u(t,x)\to 0$and$v(t,x)\to0$as$|t|+|x|\to\infty.$

Assuming the potential $V$ is bounded and has a positive bound from below, existence and multiplicity of solutions are obtained for the system with asymptotically quadratic nonlinearities via variational approach.

Citation: Yanheng Ding, Fukun Zhao. On a diffusion system with bounded potential. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1073-1086. doi: 10.3934/dcds.2009.23.1073
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