Almost Periodic Solutions of Lattice Dynamical Systems with Monotone Nonlinearity

David Cheban; Andrei Sultan

paper

Almost Periodic Solutions of Lattice Dynamical Systems with Monotone Nonlinearity

arXiv:2512.16498

Abstract

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