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On the reducibility systems of two linear first-order ordinary differential equations

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Abstract

Some global solvability criteria for the scalar Riccati equations are used to establish new reducibility criteria for systems of two linear first-order ordinary differential equations. Some examples are presented.

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References

  1. Pug, J.: Reducibility of linear equations with quasi-periodic coefficients. A survey. (May, 2002)

  2. Hou, X., You, J.: Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Inventions Mathematica 190, 208–260 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Yuan, X., Nunes, A.: A note on the reducibility of linear differential equations with quasi-periodic coefficients. IJMMS 64, 4071–4083 (2003)

    MATH  Google Scholar 

  4. Li, J., Zu, Ch.: On the reducibility of a class of finitely differentiable quasi-periodic linear systems. J. Math. Anal. Appl. 413(1), 69–83 (2014)

    Article  MathSciNet  Google Scholar 

  5. Xu, J., Kun, W., Min, Zh: On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters. Proc. Am. Math. Soc 144(11), 4793–4805 (2016)

    Article  MathSciNet  Google Scholar 

  6. Erugin, N.P.: “Reducible systems” Trudy Mat. Inst. Steklov. 13, (1946). (In Russian)

  7. Lyapunov, A.M.: Stability of motion , Acad. Press (1966) (Translated from Russian) Reducible systems. Trudy Mat. Inst. Steklov. 13, (1946). (In Russian)

  8. Grigoryan, G.A.: Boundedness and stability criteria for linear ordinary differential equations of the second order. Izv. Vyssh. Uchebn. Zaved. Mat. 12, 11–18 (2013)

    MathSciNet  Google Scholar 

  9. Grigoryan, G.A.: Two comparison criteria for scalar Riccati equations and their applications. Izv. Vyssh. Uchebn. Zaved. Mat. 11, 20–35 (2012)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics NAS of Armenia, Yerevan, Armenia

    G. A. Grigorian

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  1. G. A. Grigorian
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Correspondence to G. A. Grigorian.

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Communicated by Adrian Constantin.

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Grigorian, G.A. On the reducibility systems of two linear first-order ordinary differential equations. Monatsh Math 194, 513–522 (2021). https://doi.org/10.1007/s00605-020-01456-x

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  • DOI: https://doi.org/10.1007/s00605-020-01456-x

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