Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments

作者：Gonzalez Cristobal^*; Jimenez Melado Antonio

来源：Abstract and Applied Analysis, 2013, 2013: 957696.

DOI：10.1155/2013/957696

In this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t) = omega(t) - integral(infinity)(0) f(t, s, y(gamma(1)(s)),...,y(gamma(N)(s)))ds, t %26gt;= 0, 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 infinity as omega(l). A similar equation, but requiring a little less restrictive hypotheses, is y(t) - omega(t) - integral(infinity)(0) q(t, s)F(s, y(gamma(1)(s)),..., y(gamma(N)(s)))ds, t %26gt;= 0. In the case of q(t, s) - (t - s)(+), its solutions with asymptotic behavior given by omega(t) yield solutions of the second order nonlinear abstract differential equation y %26apos;%26apos;(t) - omega %26apos;%26apos;(t) + F(t, y(gamma(1)(t)),..., y(gamma(N)(t))) = 0, with the same asymptotic behavior at infinity as omega(t).

• 出版日期2013