Electron. J. Diff. Equ., Vol. 2014 (2014), No. 235, pp. 1-10.

Entire solutions for a mono-stable delay population model in a 2D lattice strip

Hai-Qin Zhao, San-Yang Liu

Abstract:
This article concerns the entire solutions of a mono-stable age-structured population model in a 2D lattice strip. In a previous publication, we established the existence of entire solutions related to traveling wave solutions with speeds larger than the minimal wave speed $c_{\rm min}$. However, the existence of entire solutions related to the minimal wave fronts remains open open question. In this article, we first establish a new comparison theorem. Then, applying the theorem we obtain the existence of entire solutions by mixing any finite number of traveling wave fronts with speeds $c\geq c_{\rm min}$, and a solution without the j variable. In particular, we show the relationship between the entire solution and the traveling wave fronts that they originate.

Submitted April 23, 2014. Published November 4, 2014.
Math Subject Classifications: 34K25, 35R10, 92D25.
Key Words: Entire solution; traveling wave front; delay lattice differential equation; age-structured population model.

Show me the PDF file (240 KB), TEX file, and other files for this article.

Hai-Qin Zhao
School of Mathematics and Statistics
Xidian University
Xi'an, Shaanxi 710071, China
email: hqzhao1981@hotmail.com
San-Yang Liu
School of Mathematics and Statistics
Xidian University
Xi'an, Shaanxi 710071, China
email: liusanyang@126.com

Return to the EJDE web page