# Traveling wave solutions in delayed lattice differential equations with partial monotonicity

Jianhua Huang, Gang Lu, Shigui Ruan

Research output: Contribution to journalArticle

25 Citations (Scopus)

### Abstract

In this paper, we investigate a system of delayed lattice differential equations with partial monotonicity. By using Schauder's fixed point theorem, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. Our main results can deal with the existence of traveling wave solution for a class of delayed reaction diffusion system with partial monotonicity and generalize the results of Wu and Zou (J. Differential Equations 135 (1997) 315-357).

Original language English (US) 1331-1350 20 Nonlinear Analysis 60 7 https://doi.org/10.1016/j.na.2004.10.020 Published - Mar 15 2005

### Fingerprint

Lattice Differential Equations
Delayed Differential Equation
Traveling Wave Solutions
Monotonicity
Differential equations
Partial
Schauder Fixed Point Theorem
Iteration Scheme
Reaction-diffusion System
Differential equation
Generalise

### Keywords

• Cross-iteration scheme
• Quasimonotonicity
• Schauder's fixed point theorem
• Upper and lower solutions

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics
• Mathematics(all)

### Cite this

Traveling wave solutions in delayed lattice differential equations with partial monotonicity. / Huang, Jianhua; Lu, Gang; Ruan, Shigui.

In: Nonlinear Analysis, Vol. 60, No. 7, 15.03.2005, p. 1331-1350.

Research output: Contribution to journalArticle

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