Oscillation of second-order linear delay differential equations

Ján Ohriska

Open Mathematics (2008)

  • Volume: 6, Issue: 3, page 439-452
  • ISSN: 2391-5455

Abstract

top
The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.

How to cite

top

Ján Ohriska. "Oscillation of second-order linear delay differential equations." Open Mathematics 6.3 (2008): 439-452. <http://eudml.org/doc/269394>.

@article{JánOhriska2008,
abstract = {The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.},
author = {Ján Ohriska},
journal = {Open Mathematics},
keywords = {oscillation theory; linear functional-differential equations; generalized derivatives},
language = {eng},
number = {3},
pages = {439-452},
title = {Oscillation of second-order linear delay differential equations},
url = {http://eudml.org/doc/269394},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Ján Ohriska
TI - Oscillation of second-order linear delay differential equations
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 439
EP - 452
AB - The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.
LA - eng
KW - oscillation theory; linear functional-differential equations; generalized derivatives
UR - http://eudml.org/doc/269394
ER -

References

top
  1. [1] Barrett J.H., Oscillation theory of ordinary linear differential equations, Advances in Math., 1969, 3, 415–509 http://dx.doi.org/10.1016/0001-8708(69)90008-5 
  2. [2] Džurina J., Oscillation of a second order delay differential equations, Arch. Math. (Brno), 1997, 33, 309–314 Zbl0915.34062
  3. [3] Erbe L., Oscillation criteria for second order nonlinear delay equations, Canad. Math. Bull., 1973, 16, 49–56 Zbl0272.34095
  4. [4] Hartman P., Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964 Zbl0125.32102
  5. [5] Ohriska J., Oscillation of second order delay and ordinary differential equation, Czechoslovak Math. J., 1984, 34, 107–112 Zbl0543.34054
  6. [6] Ohriska J., On the oscillation of a linear differential equation of second order, Czechoslovak Math. J., 1989, 39, 16–23 Zbl0673.34043
  7. [7] Ohriska J., Oscillation of differential equations and v-derivatives, Czechoslovak Math. J., 1989, 39, 24–44 Zbl0673.34044
  8. [8] Ohriska J., Problems with one quarter, Czechoslovak Math. J., 2005, 55, 349–363 http://dx.doi.org/10.1007/s10587-005-0026-9 Zbl1081.34033
  9. [9] Willett D., On the oscillatory behavior of the solutions of second order linear differential equations, Ann. Polon. Math., 1969, 21, 175–194 Zbl0174.13701

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.