On boundary value problems for second order ordinary differential equation with constant delay

The paper deals with establishing existence of solution theorems for boundary value problem of second order ordinary differential equation with constant delay of the type y′′(t) = f(t, y(t), y(t − r), y′(t)). We use Banach fixed point theorem to establish existence and uniqueness theorem for boundary value problem by assuming f to be Lipschitz in second, third and fourth argument. We also use Schauder’s fixed point theorem to prove existence ofsolution result for boundary value problem by assuming 'f' to be bounded.