We investigate the existence of solutions of an infinite system of integral equations of Volterra–Hammerstein type on the real half-axis. The method applied in our study is connected with the construction of a suitable measure of noncompactness in the space of continuous and bounded functions defined on the real half-axis with values in the space consisting of real sequences converging to zero and equipped with the classical supremum norm. We use the mentioned measure of noncompactness together with a fixed point theorem of Darbo type. Our investigations are illustrated by an example.
"On solutions of an infinite system of nonlinear integral equations on the real half-axis." Banach J. Math. Anal. 13 (4) 944 - 968, October 2019. https://doi.org/10.1215/17358787-2019-0008