Finite lattice approximation of infinite lattice systems with delays and non-Lipschitz nonlinearities

Article type: Research Article

Authors: Wang, Yejuan^{; *} | Sui, Meiyu

Affiliations: School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, PR China

Correspondence: [*] Corresponding author. E-mail: wangyj@lzu.edu.cn.

Abstract: In this paper, we consider the dynamics of multi-valued processes generated by nonautonomous lattice systems with delays. In particular, the effects of small delays on the asymptotic behavior of multi-valued nonautonomous lattice systems and finite lattice approximation of infinite delay lattice systems are presented. We do not assume any Lipschitiz condition on the nonlinear term, just a continuity assumption together with growth condition, so that uniqueness of solutions of the problem fails to be true.

Keywords: Pullback attractors, lattice systems with delays, set-valued dynamical system, upper semicontinuity

DOI: 10.3233/ASY-171444

Journal: Asymptotic Analysis, vol. 106, no. 3-4, pp. 169-203, 2018