Existence results of Brezis-Browder type for systems of Fredholm integral equations

In this article, we consider the following systems of Fredholm integral equations: & Iquestion presented Using an argument originating from Brezis and Browder [Bull. Am. Math. Soc. 81, 73-78 (1975)] and a fixed point theorem, we establish the existence of solutions of the first system in (C[0, T]) ⁿ, whereas for the second system, the existence criteria are developed separately in (Cl[0,∞)) ⁿ as well as in (BC[0,∞)) ⁿ. For both systems, we further seek the existence of constant-sign solutions, which include positive solutions (the usual consideration) as a special case. Several examples are also included to illustrate the results obtained.