Geodesic
Global solvability criteria for quaternionic Riccati equations
Archivum mathematicum, Tome 57 (2021) no. 2, pp. 83-99 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2021-2-83
Classification : 34C99
Keywords: Riccati equations; quaternions; the matrix representation of quaternions; global solvability; the solutions of linear systems satisfying of the completely non conjugation condition 
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Grigorian, G.A. Global solvability criteria for quaternionic Riccati equations. Archivum mathematicum, Tome 57 (2021) no. 2, pp. 83-99. doi: 10.5817/AM2021-2-83

[1] Campos, J., Mawhin, J.: Periodic solutions of quaternionic-valued ordinary differential equations. Annali di Mathematica 185 (2006), 109–127. | DOI | MR

[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

[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. | DOI | MR

[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

[5] Grigorian, G.A.: Two comparison criteria for scalar Riccati equations with applications. Russian Math. (Iz. VUZ) 56 (11) (2012), 17–30. | DOI | MR

[6] Grigorian, G.A.: Global solvability of scalar Riccati equations. Izv. Vissh. Uchebn. Zaved. Mat. 3 (2015), 35–48. | MR

[7] Grigorian, G.A.: Global solvability criteria for scalar Riccati equations with complex coefficients. Differ. Uravn. 53 (4) (2017), 459–464. | MR

[8] Hartman, Ph.: Ordinary differential equations. Classics in Applied Mathematics, vol. 38, SIAM, Philadelphia, 2002. | MR | Zbl

[9] Leschke, K., Morya, K.: Application of quaternionic holomorphic geometry to minimal surfaces. Complex Manifolds 3 (2006), 282–300. | MR

[10] Wilzinski, P.: Quaternionic - valued differential equations. The Riccati equation. J. Differential Equations 247 (2009), 2163–2187. | DOI | MR

[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. | DOI | MR

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