Advertisement

Georgian Mathematical Journal

, Volume 1, Issue 3, pp 267–276 | Cite as

Sturm's theorem for equations with delayed argument

  • A. Domoshnitsky
Article
  • 26 Downloads

Abstract

Sturm's type theorems on separation of zeros of solutions are proved for second order linear differential equations with delayed argument.

Keywords

Differential Equation Linear Differential Equation Type Theorem Order Linear Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N.V.Azbelev, About distribution of zeros of the second order differential equation with delayed argument. (Russian)Differentsial'nye Uravneniya 7(1971), No. 7, 1147–1157; English translation:Differential Equations 7(1971)Google Scholar
  2. 2.
    N.V.Azbelev and A.I.Domoshnitsky, A question concerning linear differential inequalities, II. (Russian)Differentsial'nye Uravneniya 27(1991), No. 6, 923–931; English translation:Differential Equations 27(1991), 641–647.Google Scholar
  3. 3.
    A.I.Domoshnitsky, Extension of Sturm's theorem to apply to an equation with time-lag. (Russian)Differentsial'nye Uravneniya 19(1983), No. 9, 1475–1482; English translation:Differential Equations 19(1983), 1099–1105.Google Scholar
  4. 4.
    Yu.I.Domshlak, Sturmian comparison method in investigation of behavior of solutions for differential-operator equations. (Russian) “Elm,”Baku, 1986.Google Scholar
  5. 5.
    Yu.I.Domshlak, Sturmian comparison theorem for first and second order differential equations with mixed delay of argument. (Russian)Ukrain. Mat. Zh. 34(1982), No. 2, 158–163; English translation:Ukrainian Math. J. 34(1982).Google Scholar
  6. 6.
    M.S.Du and Man Kam Kwong, Sturm comparison theorems for second order delay equations.J. Math. Anal. Appl. 152(1990), No. 2, 305–323.CrossRefGoogle Scholar
  7. 7.
    E.A.Grove, M.R.S.Kulenovic and G.Ladas, A Myshkis-type comparison result for neutral equations.Math. Nachr. 146(1990), 195–206.Google Scholar
  8. 8.
    Man Kam Kwong and W.T.Patula, Comparison theorems of first order linear delay equations.J. Differential Equations 70(1987), 275–292.CrossRefGoogle Scholar
  9. 9.
    Yu.V.Komlenko, Sufficient conditions of a regularity of the periodical boundary value problem for Hill's equations with delayed argument. (Russian)Mathematical Physics (Russian), v. 22, 5–12, “Naukova Dumka,”Kiev, 1977.Google Scholar
  10. 10.
    S.M.Labovsky, On properties of a fundamental system of second order equation with delayed argument. (Russian)Trudy Tambovskogo Instituta Khimicheskogo Mashinostroeniya 6(1971), 49–52.Google Scholar
  11. 11.
    A.D.Myshkis, Linear differential equations with delayed argument. (Russian) “Nauka,”Moscow, 1972.Google Scholar
  12. 12.
    D.V.Paatashvili On oscillation of solutions of second order differential equations with delayed arguments. (Russian)Some problems of ordinary differential equations theory (Russian),Proceedings of I.N. Vekua Institute of Applied Mathematics, v. 31, 118–129.Tbilisi University Press, Tbilisi, 1988.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. Domoshnitsky
    • 1
  1. 1.Department of Mathematics Technion CityTechnion-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations