Properties of solutions of quaternionic Riccati equations

Gevorg Avagovich Grigorian

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 2, page 115-132
  • ISSN: 0044-8753

Abstract

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In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.

How to cite

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Grigorian, Gevorg Avagovich. "Properties of solutions of quaternionic Riccati equations." Archivum Mathematicum 058.2 (2022): 115-132. <http://eudml.org/doc/298330>.

@article{Grigorian2022,
abstract = {In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.},
author = {Grigorian, Gevorg Avagovich},
journal = {Archivum Mathematicum},
keywords = {quaternions; the matrix representation of quaternions; quaternionic Riccati equations; regular; normal and extremal solutions of Riccati equations; normal; irreconci-lable; sub extremal and super extremal systems; principal and non principal solutions},
language = {eng},
number = {2},
pages = {115-132},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Properties of solutions of quaternionic Riccati equations},
url = {http://eudml.org/doc/298330},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Grigorian, Gevorg Avagovich
TI - Properties of solutions of quaternionic Riccati equations
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 2
SP - 115
EP - 132
AB - In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.
LA - eng
KW - quaternions; the matrix representation of quaternions; quaternionic Riccati equations; regular; normal and extremal solutions of Riccati equations; normal; irreconci-lable; sub extremal and super extremal systems; principal and non principal solutions
UR - http://eudml.org/doc/298330
ER -

References

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  1. Campos, J., Mavhin, J., Periodic solutions of quaternionic-valued ordinary differential equations, Ann. Math. 185 (2006), 109–127. (2006) MR2187757
  2. Christianto, V., Smarandache, F., An exact mapping from Navier-Stocks equation to Schrodinger equation via Riccati equation, Progr. Phys. 1 (2008), 38–39. (2008) MR2365963
  3. Egorov, A.I., Riccati equations, Moskow, Fizmatlit, 2001. (2001) 
  4. Gibbon, J.D., Holm, D.D., Kerr, R.M., Roulstone, I., 10.1088/0951-7715/19/8/011, Nonlinearity 19 (2006), 1962–1983. (2006) MR2250802DOI10.1088/0951-7715/19/8/011
  5. Grigorian, G. A., 10.1216/RMJ-2016-46-1-147, Rocky Mountain J. Math. 46 (1) (2016), 147–161. (2016) MR3506083DOI10.1216/RMJ-2016-46-1-147
  6. Grigorian, G.A., On some properties of solutions of the Riccati equation, Izv. Nats. Akad. Nauk Armenii Mat. 42 (4) (2007), 11–26, translation in J. Contemp. Math. Anal. 42 (2007), no. 4, 184–197. (2007) MR2413677
  7. Grigorian, G.A., On the stability of systems of two first-order linear ordinary differential equations, Differ. Uravn. 51 (3) (2015), 283–292. (2015) MR3373201
  8. Grigorian, G.A., Necessary conditions and a test for the stability of a system of two linear ordinary differential equations of the first order, Differ. Uravn. 52 (3) (2016), 292–300. (2016) MR3540205
  9. Grigorian, G.A., 10.7494/OpMath.2016.36.5.589, Opuscula Math. 36 (5) (2016), 589–601, http://dx.doi.org/10.7494/OpMath.2016.36.5.589. (2016) MR3520801DOI10.7494/OpMath.2016.36.5.589
  10. Grigorian, G.A., 10.1515/ms-2017-0274, Math. Slovaca 69 (2019), 1–14. (2019) MR3985023DOI10.1515/ms-2017-0274
  11. Grigorian, G.A., 10.5817/AM2021-2-83, Arch. Math. (Brno) 57 (2021), 83–99. (2021) MR4306170DOI10.5817/AM2021-2-83
  12. Leschke, K., Moriya, K., 10.1515/coma-2016-0015, Complex manifolds 3 (1) (2016), 282–300. (2016) MR3635782DOI10.1515/coma-2016-0015
  13. Wilzinski, P., Quaternionic-valued differential equations. The Riccati equations, J. Differential Equations 247 (2009), 2167–2187. (2009) MR2560053
  14. Zoladek, H., 10.12775/TMNA.2009.014, Topol. Methods Nonlinear Anal. 33 (2) (2009), 205–215. (2009) MR2547774DOI10.12775/TMNA.2009.014

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