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Oscillatory criteria for nonlinear $$n$$th-order differential equations with quasiderivatives. (English) Zbl 0857.34038
Author’s abstract: “Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives $$L_ny= f(t,L_0y,\dots,L_{n-1}y)$$ under the validity of the sign condition $$f(t,x_1,\dots,x_n) x_1\leq0$$, $$f(t,0,x_2,\dots,x_n)=0$$ on $$\mathbb{R}_+\times \mathbb{R}^n$$”.
Reviewer: F.Neuman (Brno)

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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##### References:
 [1] M. Bartušek and Z. Došl, Oscillatory criteria for nonlinear third-order differential equations with quasiderivatives.Diff. Eq. and Dynam. Systems (to appear). · Zbl 0869.34028 [2] T. Kusano and W. F. Trench, Global existence of nonoscillatory solutions of perturbed general disconjugate equations.Hiroshima Math. J. 17(1987), 415–431. · Zbl 0638.34028 [3] M. Švec, Behaviour of nonoscillatory solutions of some nonlinear differential equations.Acta Math.Univ. Comenian. XXXIX(1980), 115–129. [4] M. Bartušek, Asymptotic properties of oscillatory solutions of differential equations of thenth order.Folia Fak. Sci. Natur. Univ. Masarykiana Brun. Math. 3(1992). [5] I. T. Kiguradze, Some singular boundary-value problems for ordinary differential equations (Russian)Tbilisi University Press, Tbilisi, 1975. [6] I. T. Kiguradze and T. A. Chanturia, Asymptotic properties of solutions of nonautonomous ordinary differential equations. (Russian)Nauka, Moscow, 1990;English translation: Kluwer Academic Publishers, Dordrecht, 1993. [7] T. A. Chanturia, On oscillatory properties of a system of nonlinear ordinary differential equations. (Russian)Proc. I. Vekua Inst. Appl. Math. (Tbiliss. Gos. Univ. Inst. Prikl. Math. Trudy) 14(1983), 163–204. [8] M. Bartušek, On the structure of solutions of a system of three differential inequalities.Arch. Math. 30(1994), No. 2, 117–130. · Zbl 0820.34007 [9] M. Bartušek, On the structure of solutions of a system of four differential inequalities.Georgian Math. J. 2(1995), No. 3, 225–236. · Zbl 0824.34014
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