| Title:
|
Properties of solutions of quaternionic Riccati equations (English) |
| Author:
|
Grigorian, Gevorg Avagovich |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
115-132 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
quaternions |
| Keyword:
|
the matrix representation of quaternions |
| Keyword:
|
quaternionic Riccati equations |
| Keyword:
|
regular |
| Keyword:
|
normal and extremal solutions of Riccati equations |
| Keyword:
|
normal |
| Keyword:
|
irreconci-lable |
| Keyword:
|
sub extremal and super extremal systems |
| Keyword:
|
principal and non principal solutions |
| MSC:
|
34C99 |
| MSC:
|
34L30 |
| idZBL:
|
Zbl 07547205 |
| idMR:
|
MR4448487 |
| DOI:
|
10.5817/AM2022-2-115 |
| . |
| Date available:
|
2022-05-16T10:33:38Z |
| Last updated:
|
2022-08-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150425 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Egorov, A.I.: Riccati equations.Moskow, Fizmatlit, 2001. |
| Reference:
|
[4] Gibbon, J.D., Holm, D.D., Kerr, R.M., Roulstone, I.: Quaternions and periodic dynamics in the Euler fluid equations.Nonlinearity 19 (2006), 1962–1983. MR 2250802, 10.1088/0951-7715/19/8/011 |
| Reference:
|
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| Reference:
|
[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. MR 2413677 |
| Reference:
|
[7] Grigorian, G.A.: On the stability of systems of two first-order linear ordinary differential equations.Differ. Uravn. 51 (3) (2015), 283–292. MR 3373201 |
| Reference:
|
[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. MR 3540205 |
| Reference:
|
[9] Grigorian, G.A.: On one oscillatory criterion for the second order linear ordinary differential equations.Opuscula Math. 36 (5) (2016), 589–601, http://dx.doi.org/10.7494/OpMath.2016.36.5.589. MR 3520801, 10.7494/OpMath.2016.36.5.589 |
| Reference:
|
[10] Grigorian, G.A.: Oscillatory criteria for the second order linear ordinary differential equations.Math. Slovaca 69 (2019), 1–14. MR 3985023, 10.1515/ms-2017-0274 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
