Asymptotic Behavior of Slowly Varying Solutions of Second-Order Ordinary Binomial Differential Equations with Rapidly Varying Nonlinearity

Abstract

We establish new conditions for the existence of slowly varying solutions of a second-order differential binomial nonautonomous equation with rapidly varying nonlinearity. We also determine the asymptotic representations for these solutions and their first derivatives as t ↑ ω, ω ≤ + ∞.