# Article

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Keywords:
Oscillatory solution
Summary:
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.
References:
[1] 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) MR 0173060 | Zbl 0135.14302
[2] Džurina J.: The oscillation of a differential equation of second order with deviating argument. Math. Slovaca 42, No. 3 (1992), 317–324. MR 1182961 | Zbl 0756.34069
[3] Ladde G. S., Lakshmikhantam V., Zhang B. G.: Oscillation theory of differential equations with deviating arguments. Dekker, New York, 1987. MR 1017244
[4] Džurina J.: Comparison theorems for nonlinear ODEs. Math. Slovaca 42, No. 3 (1992), 299–315. MR 1182960
[5] Džurina J.: Oscillation of a second order delay differential equations. Arch. Math. (Brno) 33, No. 4 (1997), 309–314. MR 1601333
[6] Kiguradze I. T., Chanturia T. A.: Asymtotic properties of solutions of nonautonomous ordinary differential equations. Nauka, Moscow, 1990.
[7] Grace S. R.: Oscillation theorems for nonlinear differential equations of second order. J. Math. Anal. Appl. 171 (1992), 220–241. MR 1192503 | Zbl 0767.34017
[8] Philos, Ch. G.: Oscillation theorems for linear differential equations of second order. Arch. Math. (Basel) 53(5) (1989), 482–492. MR 1019162 | Zbl 0661.34030
[9] Rogovchenko, Yu. V.: Oscillation theorems for second order equations with damping. Nonlinear Anal. (1999). MR 1764033
[10] Rogovchenko, Yu. V.: Oscillation criteria for second order nonlinear perturbed differential equations. J. Math. Anal. Appl. 215 (1997), 334–357. MR 1490755 | Zbl 0892.34031
[11] Rogovchenko, Yu. V.: Oscillation criteria for certain nonlinear differential equations. J. Math. Anal. Appl. 229 (1999), 399–416. MR 1666412 | Zbl 0921.34034
[12] Yan J.: Oscillation theorems for second order linear differential equations with damping. Proc. Amer. Math. Soc. 98 (1986), 276–282. MR 0854033 | Zbl 0622.34027
[13] Agarwal R., Grace S. R., O’Regan D.: Oscillation theory for second order dynamic equations. Taylor & Francis, 2003. MR 1965832 | Zbl 1043.34032
[14] Kirane M., Rogovchenko, Yu. V.: On oscillation of nonlinear second order differential equation with damping term. Appl. Math. Comput. 117 (2001), 177–192. MR 1806045
[15] Shaker S. H.: Oscillation criteria of hyperbolic equations with deviating argument. Publ. Math. Debrecen, (2003), 165–185. MR 1956808

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