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New oscillation ciriteria of first order delay differential equations

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Języki publikacji
EN
Abstrakty
EN
In this paper we shall consider the first order delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results based on the analysis of the generalized charachterestic equation. The results partially improve some previously known results in the literature. Some examples are considered to illustrate our main results.
Słowa kluczowe
Wydawca
Rocznik
Strony
313--324
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland
autor
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland
  • Mathematical Department, Faculty of Sciences, Mansoura University, Mansoura 35516, Egypt
Bibliografia
  • [1] R. P. Agarwal, S. R. Grace and D. O'Regan, Oscillation Theory for Difference and functional Differential Equations, Kluwer, Drdrechet, 2000.
  • [2] R. P. Agarwal, S, R. Grace and D. O'Regan, Oscillation Theory for Second order Dynamic Equations, to appear.
  • [3] D. D. Bainov and D. P. Mishev, Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, New York, 1991.
  • [4] J. Chao, On the oscillation of linear differential equations with deviating arguments, Math. Practice and Theory 1 (1991), 32-40.
  • [5] K. L. Cooke and J. A. Yorke, Some equations modeling growth processes and gonorrhea epidemic, Math. Biosc. 16 (1973), 75-101.
  • [6] L. H. Erbe, Q. King and B. Z. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995.
  • [7] L. H. Erbe and B. G. Zhang, Oscillation for first order linear differential equations with deviating arguments, Differential Integral Equations 1 (1988), 305-314.
  • [8] W. K. Ergen, Kinetics of the circulating fuel nuclear reaction, J. Appl. Physics 25 (1954), 702-711.
  • [9] I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
  • [10] A. D. Heiden, Delays in Physiological Systems. In Lecture Notes in Biomathematics, Springer Verlag, 1979.
  • [11] J. Jaros and I. P. Stavroulakis, Oscillation tests for delay equations, Rocky Mountain J. Math. 29 (1999), 1-11.
  • [12] M. Kon, Y. G. Sficas and I. P. Stavroulakis, Oscillation criteria for delay equations, Proc. Amer. Math. Soc. 128 (2000), 2989-2997.
  • [13] R. G. Koplatadze and T. A. Canturija, On oscillatory and monotonia solution of first order differential equations with deviating arguments, Differentialnye Uravenenija 18 (1982), 1463-1465 (in Russian).
  • [14] M. K. Kwong, Oscillation of first order delay Equations, J. Math. Anal. Appl. (1991), 469-484.
  • [15] G. Ladas, V. Lakshmikantham and L. S. Papadakis, Oscillation of Higherorder Retarded Differential Equations Generated by the Retarded Arguments, in Delay and Functional Differential Equations and their Applications, Academic Press, New York, 1972.
  • [16] G. Ladas, Sharp conditions for oscillation caused by delays, Appl. Anal. 9 (1979), 93-98.
  • [17] G. S. Ladde, V. Lakshmikantham and B. Z. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker, New York, 1987.
  • [18] N. Macdonald, Biological Delay Systems: Linear Stability Theory, Cambridge University Press, 1989.
  • [19] A. R. Myshkis, Linear homogeneous differential equations of first order with deviating arguments, Uspehi Mat. Nauk 5 (1950), 160-162 (in Russian) (1976).
  • [20] P. I. Wangersky and J. W. Conningham, Time lag in prey-predator population models, Ecology 38 (1957), 136-139.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0043-0011
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