In this paper, we study the oscillatory behavior of the solutions of the delay differential equation of the form \[ \left(\frac{1}{r(t)}y^{\prime }(t)\right)^{\prime }+p(t)y(\tau (t))= 0. \] The obtained results are applied to n-th order delay differential equation with quasi-derivatives of the form \[ L_nu(t)+p(t)u(\tau (t))=0. \]
@article{107619, author = {Jozef D\v zurina}, title = {Oscillation of a second order delay differential equations}, journal = {Archivum Mathematicum}, volume = {033}, year = {1997}, pages = {309-314}, zbl = {0915.34062}, mrnumber = {1601333}, language = {en}, url = {http://dml.mathdoc.fr/item/107619} }
Džurina, Jozef. Oscillation of a second order delay differential equations. Archivum Mathematicum, Tome 033 (1997) pp. 309-314. http://gdmltest.u-ga.fr/item/107619/
Asymptotic properties of nonautonomous ordinary differential equations, Nauka, Moscow, 1990. (Russian) (1990)
The oscillation of a differential equation of second order with deviating argument, Math. Slovaca 42 (1992), 317–324. (1992) | MR 1182961
Comparison theorems for nonlinear ordinary differential equations, Mat. Slovaca 42 (1992), 299–315. (1992) | MR 1182960
Oscillation criteria for second order nonlinear delay equation, Canad. Math. Bull 16 (1973), 49–56. (1973) | MR 0324173
Ordinary differential equations, John Willey & Sons, New York–London–Sydney, 1964. (1964) | MR 0171038
Non-oscillation theorems, Trans.Amer.Math.Soc. 64 (1948), 234–258. (1948) | MR 0027925 | Zbl 0031.35402
Oscillation theory of differential equations with deviating arguments, Dekker, New York, 1987. (1987) | MR 1017244
Oscillation criteria for general linear ordinary differential equations, Pacific J. Math. 92 (1981), 345–355. (1981) | MR 0618070
Comparison theorems for functional differential equations with deviating arguments, J. Math. Soc. Japan 3 (1981), 509–532. (1981) | MR 0620288
On the oscillation of a linear differential equation of second order, Czech. Math. J. 39 (1989), 16–23. (1989) | MR 0983480 | Zbl 0673.34043
Oscillation of second order delay and ordinary differential equations, Czech. Math. J. 34 (1984), 107–112. (1984) | MR 0731983
Comparison and oscillation theory of linear differential equations, Acad. Press, New York-London, 1968. (1968) | MR 0463570 | Zbl 0191.09904
On certain properties of solutions of differential equations with a delay, UMŽ 24 (1972). (Ukrainian) (1972)
Asymptotic analysis of odd order ordinary differential equations, Hiroshima Math. J. 10 (1980), 391–408. (1980) | MR 0577867 | Zbl 0453.34033
Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math.Soc 189 (1974), 319–327. (1974) | MR 0330632 | Zbl 0289.34051