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Oscillation of a Class of Third-Order Neutral Differential Equations with Noncanonical Operators

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Abstract

The aim of this paper is to complement existing oscillation results for third-order neutral advanced differential equations under the condition of \(\gamma >0\); in particular, the sufficient conditions are given in different way when \(\gamma =1\). Our main idea is by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Then, combining with the results which guarantee the equation almost oscillation, we establish sufficient condition for oscillation of all solutions.

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References

  1. Chang, C.S.: PWR advanced fuel high burnup-dependent xenon oscillationcontrollability assessment. Ann. Nucl. Energy 124, 592–605 (2019)

    Article  Google Scholar 

  2. Houtte, P.V., Li, S., Seefeldt, M., et al.: Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plast. 21(3), 589–624 (2005)

    Article  Google Scholar 

  3. Bohner, M., Hassan, T.S., Li, T.: Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments. Indagationes Mathematicae 29(2), 548–560 (2018)

    Article  MathSciNet  Google Scholar 

  4. Li, T., Pintus, N., Viglialoro, G.: Properties of solutions to porous medium problems with different sources and boundary conditions. Z. Angew. Math. Phys. 70(3), 1–18 (2019)

    Article  MathSciNet  Google Scholar 

  5. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation of second-order Emden–Fowler neutral delay differential equations. Annali di Matematica 193(6), 1861–1875 (2014)

    Article  MathSciNet  Google Scholar 

  6. Agarwal, R.P., Zhang, C., Li, T.: Some remarks on oscillation of second order neutral differential equations. Appl. Math. Comput. 274, 178–181 (2016)

    MathSciNet  MATH  Google Scholar 

  7. Dzurina, J., Grace, S.R., Jadlovska, I., Li, T.: Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term. Mathematische Nachrichten 293(5), 910–922 (2020)

    Article  MathSciNet  Google Scholar 

  8. Li, T., Rogovchenko, YuV: Oscillation of second-order neutral differential equations. Mathematische Nachrichten 288(10), 1150–1162 (2015)

    Article  MathSciNet  Google Scholar 

  9. Zhang, C., Agarwal, R.P., Bohner, M., Li, T.: Oscillation of second-order nonlinear neutral dynamic equations with noncanonical operators. Bull. Malay. Math. Sci. Soc. 38(2), 761–778 (2015)

    Article  MathSciNet  Google Scholar 

  10. Li, T., Rogovchenko, YuV: On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Appl. Math. Lett. 105, 1–7 (2020)

    MathSciNet  MATH  Google Scholar 

  11. Li, T., Rogovchenko, YuV: Asymptotic behavior of higher-order quasilinear neutral differential equations. Abst. Appl. Anal. 2014, 1–11 (2014)

    MathSciNet  MATH  Google Scholar 

  12. Chatzarakis, G.E., Grace, S.R., Jadlovska, I., Li, T., Tunc, E.: Oscillation criteria for third-order Emden-Fowler differential equations with unbounded neutral coefficients. Complexity 2019, 1–7 (2019)

    Article  Google Scholar 

  13. Kiguradze, I., Chanturia, T.: Asymptotic properties of solutions of nonautonomous ordinary differential equations. Mathematics and its Applications (Soviet Series), Dordrecht (1993)

  14. Li, T., Zhang, C., Xing, G.: Oscillation of third-order neutral delay differential equations. Abst. Appl. Anal. 2012, 1–11 (2012)

    MathSciNet  MATH  Google Scholar 

  15. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation of third-order nonlinear delay differential equations. Taiwanese J. Math. 17, 545–558 (2013)

    Article  MathSciNet  Google Scholar 

  16. Dzurina, J., Grace, S.R., Jadlovská, I.: On nonexistence of Kneser solutions of third-order neutral delay differential equations. Appl. Math. Lett. 88, 193–200 (2019)

    Article  MathSciNet  Google Scholar 

  17. Dzurina, J., Jadlovská, I.: Oscillation of third-order differential equations with noncanonical operators. Appl. Math. Comput. 336, 394–402 (2018)

    Article  MathSciNet  Google Scholar 

  18. Trench, W.F.: Canonical forms and principal systems for general disconjugate equations. Trans. Am. Math. Soc. 189, 319–327 (1974)

    Article  MathSciNet  Google Scholar 

  19. Philos, C.: On the existence of nonoscillatory solutions tending to zero at \(\infty \) for differential equations with positive delays. Arch. Math. 36(2), 168–178 (1981)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript.

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Correspondence to Zhenlai Han.

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Communicated by Shangjiang Guo.

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This research is supported by the Natural Science Foundation of China (62073153, 61803176), also supported by Shandong Provincial Natural Science Foundation (ZR2020MA016)

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Feng, L., Han, Z. Oscillation of a Class of Third-Order Neutral Differential Equations with Noncanonical Operators. Bull. Malays. Math. Sci. Soc. 44, 2519–2530 (2021). https://doi.org/10.1007/s40840-021-01079-x

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  • DOI: https://doi.org/10.1007/s40840-021-01079-x

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