| Title:
|
Global solvability criteria for quaternionic Riccati equations (English) |
| Author:
|
Grigorian, G.A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
83-99 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations. (English) |
| Keyword:
|
Riccati equations |
| Keyword:
|
quaternions |
| Keyword:
|
the matrix representation of quaternions |
| Keyword:
|
global solvability |
| Keyword:
|
the solutions of linear systems satisfying of the completely non conjugation condition |
| MSC:
|
34C99 |
| idZBL:
|
Zbl 07361067 |
| idMR:
|
MR4306170 |
| DOI:
|
10.5817/AM2021-2-83 |
| . |
| Date available:
|
2021-05-11T14:22:10Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148892 |
| . |
| Reference:
|
[1] Campos, J., Mawhin, J.: Periodic solutions of quaternionic-valued ordinary differential equations.Annali di Mathematica 185 (2006), 109–127. MR 2187757, 10.1007/s10231-004-0139-z |
| Reference:
|
[2] Christiano, V., Smarandache, F.: An Exact Mapping from Navier - Stokes Equation to Schrodinger Equation via Riccati Equation.Progress in Phys. 1 (2008), 38–39. MR 2365963 |
| Reference:
|
[3] Gibbon, J.D., Halm, D.D., Kerr, R.M., Roulstone, I.: Quaternions and particle dynamics in the Euler fluid equations.Nonlinearity 19 (2006), 1962–1983. MR 2250802, 10.1088/0951-7715/19/8/011 |
| Reference:
|
[4] Grigorian, G.A.: On two comparison tests for second-order linear ordinary differential equations.Differ. Uravn. 47 (9) (2011), 1225–1240, Russian. Translation in Differ. Equ. 47 (2011), no. 9, 1237–1252. MR 2918496 |
| Reference:
|
[5] Grigorian, G.A.: Two comparison criteria for scalar Riccati equations with applications.Russian Math. (Iz. VUZ) 56 (11) (2012), 17–30. MR 3137099, 10.3103/S1066369X12110023 |
| Reference:
|
[6] Grigorian, G.A.: Global solvability of scalar Riccati equations.Izv. Vissh. Uchebn. Zaved. Mat. 3 (2015), 35–48. MR 3374339 |
| Reference:
|
[7] Grigorian, G.A.: Global solvability criteria for scalar Riccati equations with complex coefficients.Differ. Uravn. 53 (4) (2017), 459–464. MR 3657830 |
| Reference:
|
[8] Hartman, Ph.: Ordinary differential equations.Classics in Applied Mathematics, vol. 38, SIAM, Philadelphia, 2002. Zbl 1009.34001, MR 1929104 |
| Reference:
|
[9] Leschke, K., Morya, K.: Application of quaternionic holomorphic geometry to minimal surfaces.Complex Manifolds 3 (2006), 282–300. MR 3635782 |
| Reference:
|
[10] Wilzinski, P.: Quaternionic - valued differential equations. The Riccati equation.J. Differential Equations 247 (2009), 2163–2187. MR 2560053, 10.1016/j.jde.2009.06.015 |
| Reference:
|
[11] Zoladek, H.: Classifications of diffeomormhisms of $S^4$ induced by quaternionic Riccati equations with periodic coefficients.Topol. methods Nonlinear Anal. 33 (2009), 205–215. MR 2547774, 10.12775/TMNA.2009.014 |
| . |
