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



الكلمات المفتاحية:

Functional differential equation, Riemann-Stieltjes integral condition, infinite point condition, existence of solution, continuous dependence.


    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. 


Bin-Taher, E.O., (2021), the existence and uniqueness of positive solutions of an ordinary differential Equation with a nonlocal condition, Journal of Physics: Conference Series.

Byszewski, L., (1999), Existence and uniqueness of classical solution to functional-differential -abstract nonlocal cauchy problem, Journal of Applied Mathematics and Stochastic Analysis,

pp 91-97.

El-Sayed, A. M. A Hamdallah, E. and Ebead, H. (2021), on nonlocal boundary value problem of a state-dependence differential equation, Mathematics, 9, 12 pages.

El-Sayed, A. M. A ,Hamdallah, E.M. and Elkadeky, Kh. W. Monotonic positive solutions of nonlocal boundary value problems for a second order functional differential equation, Abstract and Applied Analysis,vol, (2012), Article ID 489353, 12 pages.

Goebel, K. and Kirk, W. A. (1990) Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK

Il’in, V. A. and Moiseev, E. I.(1987), A nonlocal boundary value problem of the first kind for the Sturm-Liouville operator in differential and difference interpretations, Differentsial’nye Uravneniya, vol. 23, no.7, pp. 1198–1207.

Il’in, V. A. and Moiseev, E. I. (1987) A nonlocal boundary value problem of the second kind for the Sturm-Liouville operator, Differentsial’nye Uravneniya, vol. 23, no. 8, pp. 1422–1431.

Kolmogorov, A. N. and Fomin, S. V. (1970), Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, NJ. USA.

NAJAH S ABDALLA, El-kadeky. Kh. W and SALIMA SAEID ABDALLA, Existence and uniqueness of monotonic positive solution of a functional differential equation with nonlocal conditions, Global Libyan Journal, ISSN 2518-5845,( 2022).