IJPAM: Volume 1, No. 3 (2002)

PERIODIC SOLUTIONS FOR SYSTEMS OF
TIME-DELAYED PARABOLIC EQUATIONS IN $\reals^{n}$

C.V. Pao
Dept. of Mathematics
College of Physical and Mathematical Sciences
North Carolina State University
Box 8205, Raleigh, NC 27695-8205, USA
e-mail: cvpao@math.ncsu.edu


Abstract.This paper is concerned with the existence and uniqueness of periodic solutions for a coupled system of time-delayed nonlinear parabolic equations in the space $\reals^{n}$. The approach to the problem is by the method of upper and lower solutions which leads to the existence of maximal and minimal periodic solutions for a class of nonlinear reaction functions. A sufficient condition for the uniqueness of the periodic solution is obtained. Applications are given to three reaction-diffusion models from ecology where conditions are obtained for the coexistence of the competing species.

Received: February 22, 2002

AMS Subject Classification: 35K45, 35K50, 35B10

Key Words and Phrases: time-periodic solution, parabolic system, upper and lower solutions, reaction-diffusion models, coexistence of competing species

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 3