Geodesic
Solutions of ordinary differential equations with vertical asymptote
Sbornik. Mathematics, Tome 199 (2008) no. 1, pp. 1-11 
A. A. Kon'kov. Solutions of ordinary differential equations with vertical asymptote. Sbornik. Mathematics, Tome 199 (2008) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/SM_2008_199_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions ensuring that solutions of ordinary differential equations have vertical asymptotes are obtained. Bibliography: 8 titles.

[1] L. E. Bobisud, “The distance to vertical asymptotes for solutions of second-order differential equations”, Michigan Math. J., 19:3 (1972), 277–283 | DOI | MR | Zbl

[2] S. B. Eliason, “On the distance between vertical asymptotes of solutions of a second order differential equation”, J. Math. Anal. Appl., 35:1 (1971), 148–156 | DOI | MR | Zbl

[3] I. T. Kiguradze, T. A. Chanturia, Asymptotic properties of solutions of nonautonomous ordinary differential equations, Math. Appl. (Soviet Ser.), 89, Kluwer Acad. Publ., Dordrecht, 1993 | MR | Zbl | Zbl

[4] I. T. Kiguradze, G. G. Kvinikadze, “On strongly increasing solutions of nonlinear ordinary differential equations”, Ann. Mat. Pura Appl. (4), 130:1 (1982), 67–87 | DOI | MR | Zbl

[5] “O seminare po kachestvennoi teorii differentsialnykh uravnenii v Moskovskom universitete”, Differents. uravneniya, 17:4 (1981), 749–756, V. A. Kondratev, V. S. Samovol, “O nekotorykh asimptoticheskikh svoistvakh reshenii uravnenii tipa Emdena–Faulera”

[6] A. A. Kon'kov, “On non-extendable solutions of ordinary differential equations”, J. Math. Anal. Appl., 298:1 (2004), 184–209 | DOI | MR | Zbl

[7] A. D. Myshkis, “Example of a solution of second-order differential equation of oscillatory type continuable over the entire axis”, Differential Equations, 5 (1972), 1701–1702 | MR | Zbl | Zbl

[8] L. S. Pontryagin, Ordinary differential equations, Addison-Wesley, Reading, MA–Palo Alto, CA–London, 1962 | MR | MR | Zbl | Zbl