Electron. J. Diff. Equ., Vol. 2016 (2016), No. 147, pp. 1-14.

Ground state solutions for an asymptotically linear diffusion system

Yinbin Li, Jian Zhang

Abstract:
This article concerns the diffusion system
$$\displaylines{ \partial_tu-\Delta_{x}u+V(x)u=g(t,x,v),\cr -\partial_tv-\Delta_{x}v+V(x)v=f(t,x,u), }$$
where $z=(u,v): \mathbb{R}\times \mathbb{R}^N\to \mathbb{R}^2$, $V(x)\in C(\mathbb{R}^N,\mathbb{R})$ is a general periodic function, g, f are periodic in t, x and asymptotically linear in u, v at infinity. We find a minimizing Cerami sequence of the energy functional outside the Nehari-Pankov manifold $\mathcal{N}$ and therefore obtain ground state solutions.

Submitted April 13, 2016. Published June 15, 2016.
Math Subject Classifications: 35J10, 35J20.
Key Words: Diffusion systems; asymptotically linear; diagonal method; Nehari-Pankov manifold.

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Yinbin Li
School of Mathematics and Statistics
Central South University
Changsha, Hunan 410083, China
email: liyinbin1991@163.com
Jian Zhang
School of Mathematics and Statistics
Hunan University of Commerce
Changsha, Hunan 410205, China
email: zhangjian433130@163.com

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