Oscillation of delay differential equations

J. Džurina

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1997)

  • Volume: 17, Issue: 1-2, page 97-105
  • ISSN: 1509-9407

Abstract

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

How to cite

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J. Džurina. "Oscillation of delay differential equations." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 17.1-2 (1997): 97-105. <http://eudml.org/doc/275949>.

@article{J1997,
abstract = { Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0. },
author = {J. Džurina},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {property (B); oscillation; third-order equation; delay argument; second-order delay equation},
language = {eng},
number = {1-2},
pages = {97-105},
title = {Oscillation of delay differential equations},
url = {http://eudml.org/doc/275949},
volume = {17},
year = {1997},
}

TY - JOUR
AU - J. Džurina
TI - Oscillation of delay differential equations
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1997
VL - 17
IS - 1-2
SP - 97
EP - 105
AB - Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.
LA - eng
KW - property (B); oscillation; third-order equation; delay argument; second-order delay equation
UR - http://eudml.org/doc/275949
ER -

References

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  1. [1] J. Chao, On the oscillation of linear differential equations with deviating arguments, Math. in Practice and Theory 1 (1991), 32-40. 
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  3. [3] J. Džurina, Asymptotic properties of n-th order differential equations with delayed argument Math. Nachr. 171 (1995), 149-156. Zbl0817.34039
  4. [4] J. Džurina, Comparison theorems for nonlinear ODE', Math. Slovaca. 42 (1992), 299-315. Zbl0760.34030
  5. [5] L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation Theory for Functional Differential Equations, Dekker New York 1995. Zbl0821.34067
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  8. [8] J. Jaros and I.P. Stavroulakis, Oscillation tests for delay equations, Rocky Mountain J. Math., (to appear). 
  9. [9] I.T. Kiguradze, On the oscillation of solutions of the equation d m u / d t m + a ( t ) | u | n s i g n u = 0 , Mat. Sb Russian 65 (1964), 172-187. Russian 
  10. [10] T. Kusano and M. Naito, Comparison theorems for functional differential equations with deviating arguments, J. Math. Soc. Japan. 3 (1981), 509-532. Zbl0494.34049
  11. [11] T. Kusano, M. Naito and K. Tanaka, Oscillatory and asymptotic behavior of solutions of a class of linear ordinary differential equations, Proc. Roy. Soc. Edinburgh 90 (1981), 25-40. Zbl0486.34021
  12. [12] M.K. Kwong, Oscillation of first order delay equations, J. Math. Anal. Appl. 156 (1991), 274-286. Zbl0727.34064
  13. [13] G. Ladas, Sharp conditions for oscillation caused by delay, Applicable Anal. 9 (1979), 93-982 
  14. [14] G. Ladas, V. Lakshmikantham and L.S. Papadakis, Oscillations of Higher-Order Retarded Differential Equations Generated by the Retarded Arguments, Academic Press New York 1972. Zbl0273.34052
  15. [15] G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker New York 1987. Zbl0832.34071
  16. [16] W.E. Mahfoud, Comparison theorems for delay differential equations, Pacific J. Math. 83 (1979), 187-197. Zbl0441.34053
  17. [17] W.E. Mahfoud, Oscillation and asymptotic behavior of solutions of n-th order delay differential equations, J. Diff. Eq. 24 (1977), 75-98. Zbl0341.34065

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