Traveling wave solutions in delayed lattice differential equations with partial monotonicity
Delayed lattice differential equations can be seen as the discrete version of delayed reaction-diffusion equations. In this nice paper, the authors study existence of traveling wave solutions for a system of two delayed lattice differential equations, and generalize some previous results due to \textit{J. Wu} and \textit{X. Zou} [J. Differ. Equations 135, No.2, 315-357 (1997; Zbl 0877.34046)], by relaxing the monotonicity assumptions. The main tool in their proofs is the application of Schauder's fixed-point theorem to an abstract operator defined in an appropriate subset of \(C(\mathbb{R},\mathbb{R}^2)\) endowed with an exponential decay norm.
scientific article; zbMATH DE number 2136808
scientific article