Two Point Boundary Value Problems for Nonlinear Functional Differential Equations

Abstract

This paper is concerned with the existence of solutions of two point boundary value problems for functional differential equations. Specifically, we consider \[ y’(t) = L(t,{y_t}) + f(t,{y_t}),\quad M{y_a} + N{y_b} = \psi ,\] where M and N are linear operators on $C[0,h]$. Growth conditions are imposed on f to obtain the existence of solutions. This result is then specialized to the case where $L(t,{y_t}) = A(t)y(t)$, that is, when the reduced linear equation is an ordinary rather than a functional differential equation. Several examples are discussed to illustrate the results.