Monotone iterative method for boundary value problem with linear condition of first order delay differential equation

Abstract

In this paper we discuss the boundary value problem for a first order delay differential equation of the type, \(y'(t) + \lambda y(t) = f(t, y(t - r))\). We prove the existence of solution between weakly coupled lower and upper solution by assuming \(f\) to be a non-decreasing function in the second coordinate. Further, we use this existence result to establish monotone iterative 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.