Global solvability criteria for quaternionic Riccati equations

G.A. Grigorian

Archivum Mathematicum (2021)

  • Volume: 057, Issue: 2, page 83-99
  • ISSN: 0044-8753

Abstract

top
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.

How to cite

top

Grigorian, G.A.. "Global solvability criteria for quaternionic Riccati equations." Archivum Mathematicum 057.2 (2021): 83-99. <http://eudml.org/doc/298183>.

@article{Grigorian2021,
abstract = {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.},
author = {Grigorian, G.A.},
journal = {Archivum Mathematicum},
keywords = {Riccati equations; quaternions; the matrix representation of quaternions; global solvability; the solutions of linear systems satisfying of the completely non conjugation condition},
language = {eng},
number = {2},
pages = {83-99},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Global solvability criteria for quaternionic Riccati equations},
url = {http://eudml.org/doc/298183},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Grigorian, G.A.
TI - Global solvability criteria for quaternionic Riccati equations
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 2
SP - 83
EP - 99
AB - 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.
LA - eng
KW - Riccati equations; quaternions; the matrix representation of quaternions; global solvability; the solutions of linear systems satisfying of the completely non conjugation condition
UR - http://eudml.org/doc/298183
ER -

References

top
  1. Campos, J., Mawhin, J., 10.1007/s10231-004-0139-z, Annali di Mathematica 185 (2006), 109–127. (2006) MR2187757DOI10.1007/s10231-004-0139-z
  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. (2008) MR2365963
  3. Gibbon, J.D., Halm, 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
  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. (2011) MR2918496
  5. Grigorian, G.A., 10.3103/S1066369X12110023, Russian Math. (Iz. VUZ) 56 (11) (2012), 17–30. (2012) MR3137099DOI10.3103/S1066369X12110023
  6. Grigorian, G.A., Global solvability of scalar Riccati equations, Izv. Vissh. Uchebn. Zaved. Mat. 3 (2015), 35–48. (2015) MR3374339
  7. Grigorian, G.A., Global solvability criteria for scalar Riccati equations with complex coefficients, Differ. Uravn. 53 (4) (2017), 459–464. (2017) MR3657830
  8. Hartman, Ph., Ordinary differential equations, Classics in Applied Mathematics, vol. 38, SIAM, Philadelphia, 2002. (2002) Zbl1009.34001MR1929104
  9. Leschke, K., Morya, K., Application of quaternionic holomorphic geometry to minimal surfaces, Complex Manifolds 3 (2006), 282–300. (2006) MR3635782
  10. Wilzinski, P., 10.1016/j.jde.2009.06.015, J. Differential Equations 247 (2009), 2163–2187. (2009) MR2560053DOI10.1016/j.jde.2009.06.015
  11. Zoladek, H., 10.12775/TMNA.2009.014, Topol. methods Nonlinear Anal. 33 (2009), 205–215. (2009) MR2547774DOI10.12775/TMNA.2009.014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.