Functional Differential Equation of First Order with Riemann-Stieltjes Integral and Infinite Point Nonlocal Conditions

Abstract

In this paper, by using the Schauder fixed-point theorem we study the existence of solution of the nonlocal boundary value problem of the first order functional differential equation with nonlocal conditions. The continuous dependence of the unique solution will be proved. As applications, we discuss the solution of the functional differential equation with Riemann-Stieltjes integral and infinite point nonlocal conditions. Moreover, some examples illustrate importance of the results.