Existence of solutions to infinite systems of nonlinear integral equations on the real half-axis

Abstract

In this article we study the solvability of an infinite system of integral equations of Volterra-Hammerstein type in the space of functions defined, continuous and bounded on the real half-axis with values in the sequence space l1. We extend a known existence result for such an infinite system of integral equations and prove a theorem applicable to a wider class of considered infinite systems. We also give an example to show the usefulness of our result.