Asymptotic behavior of solutions to an integral equation underlying a second-order differential equation

In this paper we propose the study of an integral equation of the type y(t)=ω(t)−∫0∞f(t,s,y(s))ds,t≥0. We investigate which conditions give existence, and which ones uniqueness, of solutions behaving like the function ω(t)ω(t) at ∞∞.In applying our results to second-order nonlinear differential equations, we are able to recover the previous results and some generalizations.