Criteria of global solvability for Riccati scalar equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2015), pp. 35-48.

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Based on two comparison theorems we prove certain coefficient criteria of global solvability for Riccati scalar equations. The result is applied to a system of two linear first-order differential equations.
Mots-clés : Riccati equation, normal and limit solutions, oscillation, non-oscillation
Keywords: regular (global) solutions, system of two linear differential first-order equations.
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G. A. Grigoryan. Criteria of global solvability for Riccati scalar equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2015), pp. 35-48. http://geodesic.mathdoc.fr/item/IVM_2015_3_a3/

[1] Erugin N. P., Kniga dlya chteniya po obschemu kursu differentsialnykh uravnenii, Nauka i tekhnika, Minsk, 1979 | MR | Zbl

[2] Erugin N. P., “Privodimye sistemy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 13, 1946, 3–96 | MR | Zbl

[3] Swanson C. A., Comparison and oscillation theory of linear differential equations, Academic Press, New York–London, 1968 | MR | Zbl

[4] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[5] Kondratev V. A., “Dostatochnye usloviya nekoleblemosti i koleblemosti reshenii uravneniya $y''+p(x)y=0$”, DAN SSSR, 113:4 (1957), 742–745 | Zbl

[6] Kamenev V. I., “Neobkhodimoe i dostatochnoe uslovie nekoleblemosti reshenii sistemy dvukh lineinykh uravnenii pervogo poryadka”, Matem. zametki, 16:2 (1974), 259–265 | MR | Zbl

[7] Stafford R. A., Heidel J. W., “A new comparison theorem for scalar Riccati equations”, Bull. Amer. Math. Soc., 80:4 (1974), 754–757 | DOI | MR | Zbl

[8] Travis C. C., “Remarks on a comparison theorem for scalar Riccati equations”, Proc. Amer. Math. Soc., 52:1 (1975), 311–314 | DOI | MR | Zbl

[9] Kwong M. K., “Integral criteria for second order linear oscillation”, Electron. J. Qual. Theory Differ. Equat., 2006, Paper No 10, 18 pp. http://www.math.u-szeged.hu/ejqtde/ | MR | Zbl

[10] Grigoryan G A., “Dva priznaka sravneniya dlya skalyarnykh uravnenii Rikkati i nekotorye ikh primeneniya”, Izv. vuzov. Matem., 2012, no. 11, 20–35 | MR | Zbl

[11] Grigoryan G. A., “Nekotorye svoistva reshenii lineinykh obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, Tr. In-ta matem. i mekhan. UrO RAN, 19, no. 1, 2013, 69–80

[12] Egorov A. I., Uravneniya Rikkati, Fizmatlit, M., 2001

[13] Grigoryan G. A., “O nekotorykh svoistvakh reshenii uravneniya Rikkati”, Izv. NAN Armenii. Matem., 42:4 (2007), 11–26 | MR | Zbl