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Global solvability of scalar Riccati equations

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Abstract

Based on two comparison theorems we obtain some coefficient characteristics of global solvability of scalar Riccati equations. The results are applied to investigation of a system of two linear first-order differential equations.

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References

  1. Erugin, N. P. A Book for Teaching Differential Equations (Nauka i Tekhnika, Minsk, 1979) [in Russian].

    Google Scholar 

  2. Erugin, N. P. “Reducible Systems,” Proc. of Steklov Math. Inst., Acad. Sci. of USSR, 13, 3–96 (1946).

    Google Scholar 

  3. Swanson, C. A. Comparison and Oscillation Theory of Linear Differential Equations (Academic Press, New York-London, 1968).

    MATH  Google Scholar 

  4. Hartman, P. Ordinary Differential Equations (John Wiley & Sons, 1964; Mir, Moscow, 1970).

    MATH  Google Scholar 

  5. Kondrat’ev, V. A. “Sufficient Conditions of Non-Oscillation and Oscillation of Solutions to the Equation y″ + p(x)y = 0,” Doklady Akad. Nauk SSSR 113, No. 4, 742–745 (1957).

    MATH  Google Scholar 

  6. Kamenev, V. I. “A Necessary and Sufficient Condition for Nonoscillatory Behavior of the Solutions to a System of two linear Equations of the First Order,” Mathematical Notes of the Academy of Sciences of the USSR 16, No. 2, 742–746 (1974).

    Article  MathSciNet  Google Scholar 

  7. Stafford, R. A., Heidel, J.W. “A New Comparison Theorem for Scalar Riccati Equations,” Bull. Amer. Math. Soc. 80, No. 4, 754–757 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  8. Travis, C. C. “Remarks on a Comparison Theorem for Scalar Riccati Equations,” Proc. Amer. Math. Soc. 52, No. 1, 311–314 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  9. Kwong, M. K. “Integral Criteria for Second-Order Linear Oscillation,” Electron. J. Qual. Theory Differ. Equat., Paper No. 10 (2006); http://www.math.u-szeged.hu/ejqtde/

    Google Scholar 

  10. Grigoryan, G. A. “Two Comparison Criteria for Scalar Riccati Equations with Applications,” Russian Mathematics (Iz. VUZ) 56, No. 11, 17–30 (2012).

    MATH  Google Scholar 

  11. Grigoryan, G. A. “Some Properties of Solutions to Second-Order Linear Ordinary Differential Equations,” Trudy Inst. Matem. i Mekh. UrO RAN, 19, No. 1, 69–80 (2013).

    Google Scholar 

  12. Egorov, A. I. Riccati Equations (Fizmatlit, Moscow, 2001) [in Russian].

    MATH  Google Scholar 

  13. Grigoryan, G. A. “On Some Properties of Solutions to Riccati Equations,” Izv. NAN Armenii. Matem. 42, No. 4, 11–26 (2007). (in Russian)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences, Republic of Armenia, pr. Marshala Bagramyana 24/5, Erevan, 0019, Republic of Armenia

    G. A. Grigoryan

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  1. G. A. Grigoryan
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Correspondence to G. A. Grigoryan.

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Original Russian Text © G.A. Grigoryan, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 3, pp. 35–48.

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Grigoryan, G.A. Global solvability of scalar Riccati equations. Russ Math. 59, 31–42 (2015). https://doi.org/10.3103/S1066369X15030044

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  • DOI: https://doi.org/10.3103/S1066369X15030044

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