Abstract In this paper, the successive approximations method is applied to solve multi-pantograph equations. The multi-pantograph equation is a kind of delay differential equations (DDEs). By this method, good approximate solutions can be obtained with only a few iteration. In addition, this method can be applied easily to solve neutral functional-differential equation with proportional delays....

and the asymptotic behaviour of its solutions. We prove that the existence and uniqueness of solutions depend mainly on the coefficients c , i s 1, 2, . . . , and on i the smoothness of functions in the solution space. As far as the asymptotic behaviour of analytic solutions is concerned, the c have little effect. We prove that i Ž . if Re a ) 0 then the solution y t either grows exponentially ...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

This paper is concerned with the stability properties of Runge–Kutta methods for the pantograph equation, a functional differential equation with a proportional delay. The focus is on nonautonomous equations. Both linear and nonlinear cases are considered. Sufficient and necessary conditions for the asymptotic stability of the numerical solution of general neutral pantograph equations are given...

In this paper, we prove a theorem on local existence and uniqueness of integral solutions to a class of partial neutral functional differential equations with infinite delay. Our method of proof is based on the integrated semigroup theory and the well known Banach fixed point theorem.