# American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems - A, 2009, 23 (3) : 1073-1086. doi: 10.3934/dcds.2009.23.1073
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