MONOTONE ITERATIVE METHOD FOR BOUNDARY VALUE PROBLEM WITH LINEAR CONDITION OF FIRST ORDER DELAY DIFFERENTIAL EQUATION.

In this paper we discuss the boundary value problem for a first order delay differential equation of the type, y(t) + y(t) = f(t, y(t - r)). We prove the existence of solution between weakly coupled lower and up- per solution by assuming f to be a non-decreasing function in the second coordinate. Further, we use this existence result to establish monotone ite- rative method, where we obtain increasing as well as decreasing sequence of functions whose limits are a solution of the boundary value problem. The sequence of functions obtained are solutions of some defined boundary value problem with linear condition of linear delay differential equation. [ABSTRACT FROM AUTHOR]