Glasgow Mathematical Journal

Research Article

On a periodic neutral logistic equation

K. Gopalsamya1, Xue-Zhong Hea2 and Lizhi Wena3

a1 School of Information Science, Flinders University, Bedford Park, S.A. 5042, Australia

a2 Department of Mathematics, Ningxia University, Yinchuan, P.R. China

a3 Department of Mathematics, South China Normal University, P.R. China

The oscillatory and asymptotic behaviour of the positive solutions of the autonomous neutral delay logistic equation

S001708950000834X_eqn1

with r, c, T, K xs2208 (0, ∞) has been recently investigated in [2]. More recently the dynamics of the periodic delay logistic equation

S001708950000834X_eqn2

in which r, K are periodic functions of period τ and m is a positive integer is considered in [6]. The purpose of the following analysis is to obtain sufficient conditions for the existence and linear asymptotic stability of a positive periodic solution of a periodic neutral delay logistic equation

S001708950000834X_eqn3

in which Ṅ denotes S001708950000834X_inline1 and r, K, c are positive continuous periodic functions of period τ at and m is a positive integer. For the origin and biological relevance of (1.3) we refer to [2].

(Received March 08 1990)