Oscillation of second-order linear delay differential equations
Ján Ohriska
Open Mathematics, Tome 6 (2008), p. 439-452 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:269394
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     author = {J\'an Ohriska},
     title = {Oscillation of second-order linear delay differential equations},
     journal = {Open Mathematics},
     volume = {6},
     year = {2008},
     pages = {439-452},
     zbl = {1153.34344},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0030-z}
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Ján Ohriska. Oscillation of second-order linear delay differential equations. Open Mathematics, Tome 6 (2008) pp. 439-452. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0030-z/

[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] Džurina J., Oscillation of a second order delay differential equations, Arch. Math. (Brno), 1997, 33, 309–314 | Zbl 0915.34062

[3] Erbe L., Oscillation criteria for second order nonlinear delay equations, Canad. Math. Bull., 1973, 16, 49–56 | Zbl 0272.34095

[4] Hartman P., Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964 | Zbl 0125.32102

[5] Ohriska J., Oscillation of second order delay and ordinary differential equation, Czechoslovak Math. J., 1984, 34, 107–112 | Zbl 0543.34054

[6] Ohriska J., On the oscillation of a linear differential equation of second order, Czechoslovak Math. J., 1989, 39, 16–23 | Zbl 0673.34043

[7] Ohriska J., Oscillation of differential equations and v-derivatives, Czechoslovak Math. J., 1989, 39, 24–44 | Zbl 0673.34044

[8] Ohriska J., Problems with one quarter, Czechoslovak Math. J., 2005, 55, 349–363 http://dx.doi.org/10.1007/s10587-005-0026-9 | Zbl 1081.34033

[9] Willett D., On the oscillatory behavior of the solutions of second order linear differential equations, Ann. Polon. Math., 1969, 21, 175–194 | Zbl 0174.13701