Some properties of the differential root and their applications
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Abstract
The denition of dierential root as a solution of the Riccati equation with a special initial value is given. A variety of properties of this solution is established, some of which generalize properties of the arithmetic square root. By using these properties we proved some boundedness and stability criteria for second order linear ordinary dierentialequations.
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Grigorian, G.
(2016).
Some properties of the differential root and their applications.
Acta Mathematica Universitatis Comenianae, 85(2), 205-217.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/226/387
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References
1. G. A. Grigorian, On two comparison tests for second-order linear ordinary dfferential equations (Russian) Differ. Uravn. 47 (2011), no. 9, 1225 - 1240;
translation in Differ. Equ. 47 (2011), no. 9 1237 - 1252, 34C10.
2. M. Gerber, B. Hasselblatt and D. Kessing. The Riccati Equation: Pinching of Forsing and Solutions "Experimental Mathematics 2003, vol. 12 No 2, pp. 129 - 134.
3. F. Hartman, Ordinary differential equations. Moscow, Mir, 1970.
4. G. A. Grigorian, On some properties of solutions of the Riccati equations (Russian) . Izv. Nats. Akad. Nauk Armenii Math. 42 (2007), no. 4, 184 - 197 34A12 (34A05).
5. M. V. Fedoryuk, Asymptotic Methods in the Theory of Ordinary linear differential equations. Nauka, Moskow, 1983 [in Russian].
translation in Differ. Equ. 47 (2011), no. 9 1237 - 1252, 34C10.
2. M. Gerber, B. Hasselblatt and D. Kessing. The Riccati Equation: Pinching of Forsing and Solutions "Experimental Mathematics 2003, vol. 12 No 2, pp. 129 - 134.
3. F. Hartman, Ordinary differential equations. Moscow, Mir, 1970.
4. G. A. Grigorian, On some properties of solutions of the Riccati equations (Russian) . Izv. Nats. Akad. Nauk Armenii Math. 42 (2007), no. 4, 184 - 197 34A12 (34A05).
5. M. V. Fedoryuk, Asymptotic Methods in the Theory of Ordinary linear differential equations. Nauka, Moskow, 1983 [in Russian].