On the construction of a nonnegative solution for one class of Urysohn-type nonlinear integral equations on a semiaxis

Abstract

We investigate a class of Urysohn-type nonlinear integral equations with noncompact operator. We assume that Wiener-Hopf-Hankel-type linear integral operator is local minorant for initial Urysohn operator. We prove alternative theorem on the existence of positive solutions and investigate asymptotic behavior of obtained solutions at infinity.