Abstract
In this paper sufficient (necessary) conditions are given under which a differential equation of the nth order has a noncontinuable solution \(y: [T, \tau) \to R, \tau < \infty\) fulfilling \(\lim_{t\to\tau_-}|y^{(j)} (t)| = \infty, j=0,1,\dots,n-1\).
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References
Bartušek, M.: On existence of singular solutions of n-th order differential equations. Arch. Math., Brno 36, 395–404 (2000)
Bartušek, M.: On existence of singular solutions. J. Math. Anal. Appl. 280, 232–240 (2003)
Bartušek, M., Osička, J.: On existence of singular solutions. Georgian Math. J. 8, 669–681 (2001)
Bartušek, M., Cecchi, M., Došlá, Z., Marini, M.: Global monotocity and oscillation for second order differential equations. Czech. Math. J. (to appear)
Coffman, C.V., Wong, J.S.W.: Oscillation and nonoscillation theorems for second order differential equations. Funkc. Ekvacioj 15, 119–130 (1972)
Izjumova, D.V., Kiguradze, I.T.: Some remarks on solutions of \(u^{\prime\prime} + a(t) f(u) = 0\). Differ. Uravn. 4, 589–605 (1968) (in Russian)
Jaroš, J., Kusano, T.: On black hole solutions of second order differential equations with a singularity in the differential operator. Funkc. Ekvacioj 43, 491–509 (2000)
Hartman, P.: Ordinary differential equations. New York, London, Sydney: Wiley 1964
Kiguradze, I.T.: Asymptotic properties of solutions of a nonlinear differential equation of Emden-Fowler type. Izv. Akad. Nauk SSSR, Ser. Math. 29, 965–986 (1965)
Kiguradze, I.T.: Remark on oscillatory solutions of \(u^{\prime\prime} + a(t) |u|^n \textit{sign}~u = 0\). Čas. Pěst. Mat. 92, 343–350 (1967)
Kiguradze, I.T., Chanturia, T.: Asymptotic properties of solution of nonautonomous ordinary differential equations. Dordrecht: Kluwer 1993
Puža, B.: On some boundary-value problems for nonlinear functional-differential equations. Differ. Uravn. 37, 761–770 (2001) (in Russian)
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Mathematics Subject Classification (2000)
34C10, 34C15, 34D05
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Bartušek, M. On the existence of unbounded noncontinuable solutions. Annali di Matematica 185 (Suppl 5), S93–S107 (2006). https://doi.org/10.1007/s10231-004-0138-0
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DOI: https://doi.org/10.1007/s10231-004-0138-0