Asymptotic Decay of the Oscillatory Solutions to First Order Non-Autonomous Linear Unstable Type Delay Differential Equations

Abstract

In this article, we are concerned with the question of the asymptotic decay of the oscillatory solutions to a class of first order linear unstable type delay differential equations with variable coefficients and constant delays. We establish a sufficient condition for all oscillatory solutions to tend to zero at ∞. This condition is substantially weaker than the one given by Ladas and the third author [Hiroshima Math. J. 18 (1988), 351-359].