Oscillation criteria for second order nonlinear differential equations
Baculíková, Blanka
Archivum Mathematicum, Tome 042 (2006), p. 141-149 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

Our aim in this paper is to present criteria for oscillation of the nonlinear differential equation \[ u^{\prime \prime }(t)+p(t)f\big (u(g(t))\big )=0\,. \] The obtained oscillatory criteria improve existing ones.

Publié le : 2006-01-01
Classification:  34C10,  34C15,  34K11 
@article{107990,
     author = {Blanka Bacul\'\i kov\'a},
     title = {Oscillation criteria for second order nonlinear differential equations},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {141-149},
     zbl = {1164.34499},
     mrnumber = {2240351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107990}
}

Baculíková, Blanka. Oscillation criteria for second order nonlinear differential equations. Archivum Mathematicum, Tome 042 (2006) pp. 141-149. http://gdmltest.u-ga.fr/item/107990/

Kiguradze I. T. On the oscillation of solutions of the equation $d^{m}u/dt^{m}+a(t)|u|^{n}sign\,u=0$, Mat. Sb. 65 (1964), 172–187. (Russian) (1964) | MR 0173060 | Zbl 0135.14302

Džurina J. The oscillation of a differential equation of second order with deviating argument, Math. Slovaca 42, No. 3 (1992), 317–324. (1992) | MR 1182961 | Zbl 0756.34069

Ladde G. S.; Lakshmikhantam V.; Zhang B. G. Oscillation theory of differential equations with deviating arguments, Dekker, New York, 1987. (1987) | MR 1017244

Džurina J. Comparison theorems for nonlinear ODEs, Math. Slovaca 42, No. 3 (1992), 299–315. (1992) | MR 1182960

Džurina J. Oscillation of a second order delay differential equations, Arch. Math. (Brno) 33, No. 4 (1997), 309–314. (1997) | MR 1601333

Kiguradze I. T.; Chanturia T. A. Asymtotic properties of solutions of nonautonomous ordinary differential equations, Nauka, Moscow, 1990. (1990)

Grace S. R. Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171 (1992), 220–241. (1992) | MR 1192503 | Zbl 0767.34017

Philos; Ch. G. Oscillation theorems for linear differential equations of second order, Arch. Math. (Basel) 53(5) (1989), 482–492. (1989) | MR 1019162 | Zbl 0661.34030

Rogovchenko; Yu. V. Oscillation theorems for second order equations with damping, Nonlinear Anal. (1999). (1999) | MR 1764033

Rogovchenko; Yu. V. Oscillation criteria for second order nonlinear perturbed differential equations, J. Math. Anal. Appl. 215 (1997), 334–357. (1997) | MR 1490755 | Zbl 0892.34031

Rogovchenko; Yu. V. Oscillation criteria for certain nonlinear differential equations, J. Math. Anal. Appl. 229 (1999), 399–416. (1999) | MR 1666412 | Zbl 0921.34034

Yan J. Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986), 276–282. (1986) | MR 0854033 | Zbl 0622.34027

Agarwal R.; Grace S. R.; O’Regan D. Oscillation theory for second order dynamic equations, Taylor & Francis, 2003. | MR 1965832 | Zbl 1043.34032

Kirane M.; Rogovchenko; Yu. V. On oscillation of nonlinear second order differential equation with damping term, Appl. Math. Comput. 117 (2001), 177–192. (192.) | MR 1806045

Shaker S. H. Oscillation criteria of hyperbolic equations with deviating argument, Publ. Math. Debrecen, (2003), 165–185. | MR 1956808