Asymptotic stability of solutions to an infinite system of Volterra–Urysohn–Stieltjes integral equations

Source abstract

In this paper, we study two problems related to an infinite system of quadratic Urysohn integral equations of Stieltjes type. First, we establish the existence of solutions to such a system in the Banach space of bounded and continuous functions taking values in the Banach space of bounded real sequences. Second, we characterize the solutions to this infinite system in terms of asymptotic stability. The results obtained in this paper provide a significant extension of earlier findings for infinite systems of classical integral equations of both Hammerstein and Urysohn types.