P. Nesterov, "Asymptotic Integration of Certain Volterra Integro-Differential Equations with Oscillatory Decreasing Kernels", принято к публикации в журнале Differential Equations and Dynamical Systems.
We construct the asymptotics for solutions of two second-order integro-differential equations of Volterra type as independent variable tends to infinity. These equations are considered as integral perturbations of the harmonic oscillator. The specific feature of the considered integral perturbations is an oscillatory decreasing character of their kernels. To obtain the asymptotic formulas we use the special method proposed for the asymptotic integration of the linear dynamical systems with oscillatory decreasing coefficients. The method uses the ideas of the averaging theory and some known asymptotic theorems.