Siberian Mathematical Journal

, Volume 60, Issue 4, pp 636–643 | Cite as

Tests for the Oscillation of Autonomous Differential Equations with Bounded Aftereffect

  • V. V. MalyginaEmail author


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.


delay differential equation oscillation concentrated and distributed delay 


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  1. 1.
    Chaplygin S. A., A New Method of Approximate Integration of Differential Equations [Russian], Gostekhizdat, Moscow and Leningrad (1950).Google Scholar
  2. 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).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F., Introduction to the Theory of Functional-Differential Equations [Russian], Nauka, Moscow (1991).zbMATHGoogle Scholar
  4. 4.
    Győri I. and Ladas G., Oscillation Theory of Delay Differential Equations with Applications, The Clarendon Press and Oxford Univ. Press, New York (1991).zbMATHGoogle Scholar
  5. 5.
    Sabatulina T. L., “Oscillating solutions of autonomous differential equations with aftereffect,” Vestn. Permsk. Univ. Mat. Mekh. Inform., no. 3, 25–32 (2016).Google Scholar
  6. 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).Google Scholar
  7. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Li B., “Oscillation of first order delay differential equations,” Proc. Amer. Math. Soc., vol. 124, no. 12, 3729–3737 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Berezansky L. and Braverman E., “Oscillation of equations with an infinite distributed delay,” Comp. Math. Appl., vol. 60, 2583–2593 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Natanson I. P., Theory of Functions of Real Variable, Ungar, New York (1955).zbMATHGoogle Scholar

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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

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