Abstract
In this study, new asymptotic properties of positive solutions of the even-order delay differential equation with the noncanonical operator are established. The new properties are of an iterative nature, which allows it to be applied several times. Moreover, we use these properties to obtain new criteria for the oscillation of the solutions of the studied equation using the principles of comparison.
Highlights
Our interest in this work revolves around the study of the asymptotic behavior of positive solutions of the delay differential equation (DDE): d dt a·
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Using Theorem 3, we obtain that Equation (13) has a positive solution, a contradiction
Summary
New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application. Our interest in this work revolves around the study of the asymptotic behavior of positive solutions of the delay differential equation (DDE): d dt a· By establishing comparison theorems that compare the nth-order equation with one or a couple of first-order delay differential equations, Baculíková et al [19] studied the oscillatory properties of the DDE: (a(t)(ψ(n−1)(t))γ) + q(t) f (ψ(g(t))) = 0, (3) We first obtain new asymptotic properties of the positive solutions of DDE (1).
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