Solvability of an infinite system of integral equations on the real half-axis

Abstract

<jats:title>Abstract</jats:title><jats:p>The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space <jats:italic>l</jats:italic><jats:sub>∞</jats:sub> consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space <jats:italic>l</jats:italic><jats:sub>∞</jats:sub>. An example illustrating our result will be included.</jats:p>

A New Survey of Measures of Noncompactness and Their Applications

“…where t ∈ R + and n ∈ N, on the real half-axis ([63], Theorem 3.4). The paper [63] is in continuation of the papers [64,65].…”

“…In [63], the authors construct a measure of noncompactness on the space BC(R + , ∞ ) of all functions x : R + → ∞ that are continuous and bounded on R…”