On the Weak Solutions of the Urysohn-Stieltjes Functional Integral Equations

Abstract

The analysis of Urysohn-Stieltjes integral operators has been studied in [1]. Here we study the existence of weakly solution of functional integral equations of Urysohn-Stieltjes type and Hammerstien-Stieltjes type in the reflexive Banach space E. Also, we prove the existence of the weak maximal and weak minimal solutions.

Weak Solutions of a Coupled System of Urysohn‐Stieltjes Functional (Delayed) Integral Equations

“…We remark here that when E = R, these types of equations have been studied by Banaś (see [1][2][3][4][5]) and also by some other authors, for example (see [6][7][8][9][10] and for coupled systems [11]). For the solutions in a reflexive Banach space (see [12,13]). In this paper, let ψ i t ≤ t be continuous functions on 0, 1 We generalize these results to study the existence of weak solutions x, y ∈ C I, E × C I, E for the coupled system of Urysohn-Stieltjes functional (delayed) integral equations: As an application, we study the existence of weak solutions x, y ∈ C I, E for the coupled system of Hammerstien-Stieltjes functional integral equations:…”