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Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Volume: 13 Issue: 2

Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Nurten Kılıç(DUMLUPINAR ÜNİVERSİTESİ)0000-0001-9632-6651
Pages
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Publication Date
2021-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also give an example illustrating the result.

📌 3 Key Takeaways

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Objective & Hypothesis:In this article, we analyze the first order linear delay differential equation \begin{equation*} x^{\prime }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\geq t_{0}, \end{equation*} where $p,$ $\tau \in C\left( [t_{0},\infty ),\mathbb{R}^{+}\right) $ and $% \tau (t)\leq t,\ \lim_{t\rightarrow \infty }\tau (t)=\infty $.
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Key Findings & Data:Under the assumption that $\tau (t)$ is not necessarily monotone, we obtain new sufficient criterion for the oscillatory solutions of this equation.
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Conclusion & Impact:We also give an example illustrating the result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Delay equation · nonmonotone argument · oscillatory solution

Abstract

In this article, we analyze the first order linear delay differential equation \begin{equation*} x^{\prime }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\geq t_{0}, \end{equation*} where $p,$ $\tau \in C\left( [t_{0},\infty ),\mathbb{R}^{+}\right) $ and $% \tau (t)\leq t,\ \lim_{t\rightarrow \infty }\tau (t)=\infty $. Under the assumption that $\tau (t)$ is not necessarily monotone, we obtain new sufficient criterion for the oscillatory solutions of this equation. We also give an example illustrating the result.

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Cite This Article

Kılıç, N. (2021). Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument. Turkish Journal of Mathematics and Computer Science, Volume: 13 Issue: 2. https://doi.org/10.47000/tjmcs.893395

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References (17)

  1. Akca, H., Chatzarakis, G.E., Stavroulakis, I.P., An oscillation criterion for delay differential equations with several non-monotone arguments, Applied Mathematics Letters, 59(2016), 101–108.
  2. Chatzarakis, G.E., Peics, H., Differential equations with several non-monotone arguments: An oscillation result, Applied Mathematics Letters, 68(2017), 20–26.
  3. Chao, J., On the oscillation of linear differential equations with deviating arguments, Math. in Practice and Theory, 1(1991), 32-40.
  4. Elbert, A., Stavroulakis, I.P., Oscillations of first order differential equations with deviating arguments, University of Ioannina, T.R. No 172 1990, Recent trends in differential equations, 163-178, World Sci. Ser. Appl. Anal., 1, World Sci. Publishing Co., 1992.
  5. Erbe, L.H., Zhang, B.G., Oscillation of first order linear differential equations with deviating arguments, Differ. Integral Equ., 1(1988), 305–314.
  6. Erbe, L.H., Kong, Q., Zhang, B.G., Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995.
  7. Fukagai, N., Kusano, T., Oscillation theory of first order functional differential equations with deviating arguments, Ann. Mat. Pura Appl., 136(1984), 95-117.
  8. Györi, I., Ladas, G., Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
  9. Jaros, J., Stavroulakis, I.P., Oscillation tests for delay equations, Rocky Mountain J. Math., 29(1999), 139–145.
  10. Kon, M., Sficas, Y.G., Stavroulakis, I.P., Oscillation criteria for delay equations, Proc. Amer. Math. Soc., 128(2000), 2989–2997.
  11. Koplatadze, R.G., Chanturija, T.A., Oscillating and monotone solutions of first-order differential equations with deviating arguments, (Russian), Differentsial’nye Uravneniya, 8(1982), 1463-1465.
  12. Koplatadze, R., Kvinikadze, G., On the oscillation of solutions of first order delay diferential inequalities and equations, Georgian Mathematical Journal, 1(6)(1994), 675–685.
  13. Kwong, M.K., Oscillation of first-order delay equations, J. Math. Anal. Appl., 156(1991), 274–286.
  14. Ladde, G.S., Lakshmikantham, V., Zhang, B.G., Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics, vol. 110, Marcel Dekker, Inc., New York, 1987.
  15. Philos, Ch.G., Sficas, Y.G., An oscillation criterion for first order linear delay differential equations, Canad. Math. Bull. 41(1998), 207-213.
  16. Yu, J.S., Wang, Z.C., Some further results on oscillation of neutral differential equations, Bull. Aust. Math. Soc., 46(1992), 149–157.
  17. Yu, J.S.,Wang, Z.C., Zhang, B.G., Qian, X.Z., Oscillations of differential equations with deviating arguments, PanAmerican Math. J., 2(1992), 59–78.