In this paper, we propose the study of an integral equation, with deviating arguments, of the type in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at as . A similar equation, but requiring a little less restrictive hypotheses, is In the case of , its solutions with asymptotic behavior given by yield solutions of the second order nonlinear abstract differential equation with the same asymptotic behavior at as .
"Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments." Abstr. Appl. Anal. 2013 (SI28) 1 - 7, 2013. https://doi.org/10.1155/2013/957696