A nonlinear Volterra equation with rapidly decaying solutions

Abstract

We study the asymptotic behavior of the solutions of a nonlinear integrodifferential Volterra equation with a convolution kernel. More specifically, we give conditions which imply that a solution x satisfies x ( t ) = O ( t − p ) ( t → ∞ ) x(t)\, = \,O({t^{ - p}})\,(t \to \infty ) , where p is an arbitrary, positive real number.