Abstract
We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach spaceE. As an application, the coupled system of Hammerstien-Stieltjes functional integral equations is also studied.
Highlights
Introduction and PreliminariesConsider the Urysohn-Stieltjes integral equation:x t = p t + f t, s, x s dsg t, s, t ∈ I = 0, 1, where g I × I → R is nondecreasing in the second argument and the symbol ds indicates the integration with respect to s
We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach space E
Consider the Urysohn-Stieltjes integral equation: x t = p t + f t, s, x s dsg t, s, t ∈ I = 0, 1, where g I × I → R is nondecreasing in the second argument and the symbol ds indicates the integration with respect to s
Summary
We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach space E. 0, 1InWtheigsenpearpaelriz,eletht eψsei t ≤t results be to continuous functions on 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: x t = a1 t + f1 t, s, y ψ1 s dsg1 t, s , t ∈ I, 0 1 yt We study the existence of weak solutions x, y ∈ C I, E for the coupled system of HammerstienStieltjes functional integral equations: xt
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