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Tests for the Oscillation of Autonomous Differential Equations with Bounded Aftereffect

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Abstract

Considering autonomous delay functional differential equations, we establish some oscillation criterion that reduces the oscillation problem to computing the only root of the real-valued function defined by the coefficients of the initial equation. Using the criterion, we obtain effectively verifiable oscillation tests for equations with various aftereffects.

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References

  1. Chaplygin S. A., A New Method of Approximate Integration of Differential Equations [Russian], Gostekhizdat, Moscow and Leningrad (1950).

    Google Scholar 

  2. Myshkis A. D., “On solutions of linear homogeneous differential equations of the second order of periodic type with a retarded argument,” Mat. Sb., vol. 28, no. 3, 641–658 (1951).

    MathSciNet  MATH  Google Scholar 

  3. Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F., Introduction to the Theory of Functional-Differential Equations [Russian], Nauka, Moscow (1991).

    MATH  Google Scholar 

  4. Győri I. and Ladas G., Oscillation Theory of Delay Differential Equations with Applications, The Clarendon Press and Oxford Univ. Press, New York (1991).

    MATH  Google Scholar 

  5. Sabatulina T. L., “Oscillating solutions of autonomous differential equations with aftereffect,” Vestn. Permsk. Univ. Mat. Mekh. Inform., no. 3, 25–32 (2016).

  6. Tramov M. I., “Conditions for the oscillation of the solutions of first order differential equations with retarded argument,” Izv. Vyssh. Uchebn. Zaved. Mat., no. 3, 92–96 (1975).

  7. Koplatadze R. and Kvinikadze G., “On oscillation of solutions of first order delay differential inequalities and equations,” Georgian Math. J., vol. 1, 675–685 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  8. Li B., “Oscillation of first order delay differential equations,” Proc. Amer. Math. Soc., vol. 124, no. 12, 3729–3737 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  9. Tang X. H., “Oscillation of first order delay differential equations with distributed delay,” J. Math. Anal. Appl., vol. 289, no. 2, 367–378 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  10. Berezansky L. and Braverman E., “Oscillation of equations with an infinite distributed delay,” Comp. Math. Appl., vol. 60, 2583–2593 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  11. Chudinov K. M., “On exact sufficient oscillation conditions for solutions of linear differential and difference equations of the first order with aftereffect,” Russian Math. (Iz. VUZ), vol. 62, no. 5, 79–84 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  12. Sabatulina T. and Malygina V., “On positiveness of the fundamental solution for a linear autonomous differential equation with distributed delay,” Electron. J. Qual. Theory Differ. Equ., vol. 61, 1–16 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  13. Natanson I. P., Theory of Functions of Real Variable, Ungar, New York (1955).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Perm National Research Polytechnic University, Perm, Russia

    V. V. Malygina

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  1. V. V. Malygina
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Correspondence to V. V. Malygina.

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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 4, pp. 815–823.

The author was supported by the Ministry of Education and Science of the Russian Federation by the State Assignment No. 1.5336.2017/8.9 with the support of the Russian Foundation for Basic Research (Grant 18-01-00928).

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Malygina, V.V. Tests for the Oscillation of Autonomous Differential Equations with Bounded Aftereffect. Sib Math J 60, 636–643 (2019). https://doi.org/10.1134/S0037446619040098

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  • DOI: https://doi.org/10.1134/S0037446619040098

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