On zeros of solutions of nonlinear nonautonomous ordinary differential equations of second order

N.V. Varekh (Dnipropetrovsk State University)
V.N. Shevelo (Dnipropetrovsk State University)

Abstract


On zeros of solutions of nonlinear nonautonomous ordinary differential equations of second order.

References


Shevelo V.N. "On research in oscillation properties of solutions of nonlinear nonautonomous ordinary differential equations of order $$$n$$$ by first approximation", Bull. of Internat. Math. Congress, 1966; 8: p. 4. (in Russian)

Shevelo V.N., Varekh N.V. "On some properties of solutions of nonlinear nonautonomous ordinary differential equations of second order", in: Matem. fizika, Naukova dumka, 1967; pp. 237-247. (in Russian)

Levin A.Yu. "Integral criterion of non-oscillation for the equation $$$\ddot{x} + q(t)x = 0$$$.", Uspekhi matem. nauk, 1965; 20(2): pp. 244-246. (in Russian)

Leighton W. "On the zeros of solutions of a second order linear differential equations", J. de Math. Pure Appl., 1965; 44(3): pp. 293-300.

Galbraith A.S. "On the zeros of solutions of ordinary differential equations of the second order", Proc. Amer. Math. Soc., 1966; 17(2): pp. 333-337. doi:10.2307/2035161

Wintner A. "On the non-existence of conjugate points", Amer. J. Math., 1951; 73(2): pp. 368-380. doi:10.2307/2372182

Shevelo V.N., Shtelik V.G. "Some questions of oscillation of solutions of nonlinear nonautonomous equations of second order", Dokl. AN SSSR, 1963; 149(2): pp. 276-279. (in Russian)

Szmydt Z. "Sur l'allure asumptotique des integrales des certeins systems equations differentelles non lineaires", Ann. Polon. Math., 1955; 1, 2: pp. 253-276.

Hartman P., Wintner A. "Asymptotic integrations of linear differential equations", Amer. J. Math., 1955; 77(1): pp. 45-86. doi:10.2307/2372422

Olech C. "On the asymptotic behaviour of the solutions of a system of ordinary non-linear differential equations", Bull. Acad. Polon. Sci., 1960; 111(4): pp. 555-561.

Brauer F. "Asymptotic equivalence and asymptotic behaviour of linear systems", Michigan J. Math., 1962; 9: pp. 33-43. doi:10.1307/mmj/1028998618

Waltman P. "On the asymptotic behavior of solutions of a nonlinear equation", Proc. Amer. Math. Soc., 1964; 15(6): pp. 918-923. doi:10.2307/2034909

Kiguradze I.T. "Asymptotic properties of solutions of one nonlinear differential equation of Emden-Fowler type", Izv. AN SSSR, 1965; 29: pp. 965-986. (in Russian)

Onuchic N. "Asymptotic relationships at infinity between the solutions of two systems of ordinary differential equations", J. Diff. Equat., 1967; 3(1): pp. 47-58. doi:10.1016/0022-0396(67)90005-8




DOI: https://doi.org/10.15421/246706

  

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Copyright (c) 1967 N.V. Varekh, V.N. Shevelo

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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