On the absence of global solutions of a system of ordinary differential equations
Sbornik. Mathematics, Tome 213 (2022) no. 3, pp. 319-340 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions for the absence of global solutions of a system of nonlinear ordinary differential equations are found. Examples showing that these conditions are sharp are given. Bibliography: 12 titles.
Keywords: systems of nonlinear ordinary differential equations, blow-up, estimates for solutions.
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A. A. Kon'kov. On the absence of global solutions of a system of ordinary differential equations. Sbornik. Mathematics, Tome 213 (2022) no. 3, pp. 319-340. http://geodesic.mathdoc.fr/item/SM_2022_213_3_a2/

[1] I. Astashova, “On power and non-power asymptotic behavior of positive solutions to Emden–Fowler type higher-order equations”, Adv. Difference Equ., 2013 (2013), 220, 15 pp. | DOI | MR | Zbl

[2] I. Astashova, “On quasi-periodic solutions to a higher-order Emden–Fowler type differential equation”, Bound. Value Probl., 2014 (2014), 174, 8 pp. | DOI | MR | Zbl

[3] A. L. Gladkov, A. I. Nikitin, “On the existence of global solutions of a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions”, Differ. Equ., 52:4 (2016), 467–482 | DOI | DOI | MR | Zbl

[4] A. L. Gladkov, N. L. Slepchenkov, “On proper and entire solutions of a generalized Emden–Fowler equation”, Differ. Equ., 41:2 (2005), 173–183 | DOI | MR | Zbl

[5] N. A. Izobov, “Extendable and nonextendable solutions of a nonlinear differential equation of arbitrary order”, Math. Notes, 35:6 (1984), 435–441 | DOI | MR | Zbl

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

[7] 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, xiv+331 pp. | DOI | MR | Zbl | Zbl

[8] A. A. Kon'kov, “On solutions of non-autonomous ordinary differential equations”, Izv. Math., 65:2 (2001), 285–327 | DOI | DOI | MR | Zbl

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

[10] A. A. Kon'kov, “A priori estimates for solutions of ordinary differential equations of Emden–Fowler type”, Math. Notes, 73:5 (2003), 747–750 | DOI | DOI | MR | Zbl

[11] V. A. Rabtsevich, “Nonoscillating unbounded solutions of Emden–Fowler systems of arbitrary order”, Differ. Equ., 36:1 (2000), 97–107 | DOI | MR | Zbl

[12] C. S. Yarur, “On the behavior of positive solutions for a class of semilinear elliptic systems”, Reaction diffusion systems (Trieste, 1995), Lecture Notes in Pure and Appl. Math., 194, Dekker, New York, 1998, 401–409 | MR | Zbl