Oscillation of second-order nonlinear neutral delay dynamic equations on time scales

By Samir H. Saker. 2006

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In this paper, some sufficient conditions for oscillation of the second-order nonlinear neutral delay dynamic equation (r(t)([y(t) + p(t)y(t - τ)]Δ)γ)Δ + f(t, y(t - δ)) = 0, on a time scale T are established; here γ ≥ 1 is an odd positive integer with r(t) and p(t) are rd-continuous functions defined on T. Our results as a special case when T = R and T = N, involve and improve some well-known oscillation results for second-order neutral delay differential and difference equations. When T = hN and T = qN = {t: t = qk, k ∈ N, q > 1}, i.e., for generalized neutral delay difference and q-neutral delay difference equations our results are essentially new and also can be applied on different types of time scales, e.g., T = N2 = {t2 : t ∈ N} and T = Tn = {tn: n ∈ N0} where {tn} is the set of harmonic numbers. Some examples illustrating our main results are given.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3761582031a988b3b2945ba04a0c58e4f4f1c352

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In Applied Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Hille and Nehari type criteria for third-order delay dynamic equations (2013, methodology): “We refer the reader to the papers [1–3,6,7,9–12,22–28] and references cited therein.”