Electron. J. Diff. Equ., Vol. 2013 (2013), No. 120, pp. 1-8.

Existence of entire solutions for non-local delayed lattice differential equations

Shi-Liang Wu, San-Yang Liu

Abstract:
In this article we study entire solutions for a non-local delayed lattice differential equation with monostable nonlinearity. First, based on a concavity assumption of the birth function, we establish a comparison theorem. Then, applying the comparison theorem, we show the existence and some qualitative features of entire solutions by mixing a finite number of traveling wave fronts with a spatially independent solution.

Submitted March 18, 2013. Published May 16, 2013.
Math Subject Classifications: 35B40, 35R10, 37L60, 58D25.
Key Words: Entire solution; traveling wave front; monostable nonlinearity; non-local delayed lattice differential equation.

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Shi-Liang Wu
Department of Mathematics, Xidian University
Xi'an, Shaanxi 710071, China
email: slwu@xidian.edu.cn
San-Yang Liu
Department of Mathematics, Xidian University
Xi'an, Shaanxi 710071, China
email: liusanyang@126.com

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