Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 717–723 | Cite as

Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect

  • V. V. Malygina


For autonomous functional-differential equations with delays, we obtain an oscillation criterion, which allows one to reduce the oscillation problem to the calculation of a unique root of a real-valued function determined by the coefficients of the original equation. The criterion is illustrated by examples of equations with concentrated and distributed aftereffect, for which convenient oscillation tests are obtained.

Keywords and phrases

differential equation with aftereffect oscillation concentrated and distributed delay 

AMS Subject Classification

34K06 34K11 


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  1. 1.
    N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Linear Functional Differential Equations, World Federation Publ., Atlanta (1995).zbMATHGoogle Scholar
  2. 2.
    I. Győri and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, The Clarendon Press, Oxford Univ. Press, New York (1991).zbMATHGoogle Scholar
  3. 3.
    A. D. Myshkis, “On solutions of first-order linear homogeneous differential equations of stable type with delayed argument,” Mat. Sb., 28, No. 3, 641–658 (1951).zbMATHGoogle Scholar
  4. 4.
    T. L. Sabatulina, “On oscillating solutions of autonomous differential equations with aftereffect,” Vestn. Perm. Univ., 3 (34), 25–31 (2016).Google Scholar
  5. 5.
    T. Sabatulina and V. Malygina, “On positiveness of the fundamental solution for a linear autonomous differential equation with distributed delay,” Electron. J. Qual. Theory Differ. Equ., 61, 1–16 (2014).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

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