Asymptotic expansion for the initial value problem of the sunflower equation

Abstract

In this paper, we consider the initial value problem (IVP) for the sunflower equation, εx″( t) + ax′( t) + b sin x( t − ε) = 0, with x( t) = ϕ( t), t ϵ [− ε, 0]; x′(0) = y 0. We prove that the solution of the above-mentioned IVP has an asymptotic expansion uniformly valid on [−ε, ∞), for ε sufficiently small.