N(t) = r(t)N(t) a ~ bkN(hk(t)) cl(t)N(gl(t)), k ~ l l = l N(t)=~(t) , t O , is considered. The existence and the bounds of positive solutions are studied. Sufficient conditions for the extinction of the solution are presented. © 2004 Elsevier Ltd. All rights reserved. K e y w o r d s D e l a y logistic equations, Linear harvesting, Positive solutions, Extinction of the populatio...

This article concerns delay–differential equations (DDEs) with constant lags. DDEs increasingly are being used to model various phenomena in mathematics and the physical sciences. For such equations the value of the derivative at any time depends on the solution at a previous “lagged” time. Although solving DDEs is similar in some respects to solving ordinary differential equations (ODEs), it d...

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

MANUEL PINTO Departamento de Matemiticas Facultad de Ciencias Universidad de Chile Casilla 653 Santiago, CHILE (Received October 4, 1994 and in revised form April 6,1995) ABSTRACT. Asymptotic formulae for the solutions of nonlinear functional differential system are obtained.

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

Ordinary differential equations (ODEs) and delay differential equations (DDEs) are used to describe many phenomena of physical interest. While ODEs contain derivatives which depend on the solution at the present value of the independent variable (“time”), DDEs contain in addition derivatives which depend on the solution at previous times. DDEs arise in models throughout the sciences [1]. Despit...

Delay or queue length information has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on d...