Almost Periodic Solutions of Lattice Dynamical Systems with Monotone Nonlinearity

Abstract

The aim of this paper is studying the problem of almost periodicity of almost periodic lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z,\ \lambda >0)$. We prove the existence a unique almost periodic solution of this system if the nonlinearity $F$ is monotone.