Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations

Gevorg Avagovich Grigorian

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 4, page 189-203
  • ISSN: 0044-8753

Abstract

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The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example, one of the obtained oscillatory criteria is compared with some well known results.

How to cite

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Grigorian, Gevorg Avagovich. "Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations." Archivum Mathematicum 054.4 (2018): 189-203. <http://eudml.org/doc/294453>.

@article{Grigorian2018,
abstract = {The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example, one of the obtained oscillatory criteria is compared with some well known results.},
author = {Grigorian, Gevorg Avagovich},
journal = {Archivum Mathematicum},
keywords = {Riccati equation; oscillation; non oscillation; prepared (preferred) solution; Liouville’s formula},
language = {eng},
number = {4},
pages = {189-203},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations},
url = {http://eudml.org/doc/294453},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Grigorian, Gevorg Avagovich
TI - Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 4
SP - 189
EP - 203
AB - The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example, one of the obtained oscillatory criteria is compared with some well known results.
LA - eng
KW - Riccati equation; oscillation; non oscillation; prepared (preferred) solution; Liouville’s formula
UR - http://eudml.org/doc/294453
ER -

References

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  1. Butler, G.J., Erbe, L.H., Mingarelli, A.B., 10.1090/S0002-9947-1987-0896022-5, Trans. Amer. Math. Soc. 303 (1) (1987), 263–282. (1987) MR0896022DOI10.1090/S0002-9947-1987-0896022-5
  2. Byers, R., Harris, B.J., Kwong, M.K., 10.1016/0022-0396(86)90117-8, J. Differential Equations 61 (1986), 164–177. (1986) MR0823400DOI10.1016/0022-0396(86)90117-8
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  4. Grigorian, G.A., 10.1134/S0012266111090023, Differ. Uravn. 47 (2011), 1225–1240, translation in Differential Equations 47 (2011), no. 9 1237–1252. (2011) MR2918496DOI10.1134/S0012266111090023
  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. Vyssh. Uchebn. Zaved. Mat. 3 (2015), 35–48. (2015) MR3374339
  7. Grigorian, G.A., 10.1134/S0012266115030015, Differ. Uravn. 51 (3) (2015), 283–292. (2015) MR3373201DOI10.1134/S0012266115030015
  8. 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
  9. Hartman, P., Ordinary differential equations, Classics Appl. Math., SIAM 38 (2002). (2002) Zbl1009.34001MR1929104
  10. Li, L., Meng, F., Zhung, Z., Oscillation results related to integral averaging technique for linear hamiltonian system, Dynam. Systems Appl. 18 (2009), 725–736. (2009) MR2562259
  11. Meng, F., Mingarelli, A.B., 10.1090/S0002-9939-02-06614-5, Proc. Amer. Math. Soc. 131 (3) (2002), 897–904. (2002) MR1937428DOI10.1090/S0002-9939-02-06614-5
  12. Mingarelli, A.B., On a conjecture for oscillation of second order ordinary differential systems, Proc. Amer. Math. Soc. 82 (4), 593–598. MR0614884
  13. Wang, Q., 10.1007/PL00000448, Arch. Math. (Basel) 76 (2001), 385–390. (2001) MR1824258DOI10.1007/PL00000448
  14. Zhung, Z., Zhu, S., Hartman type oscillation criteria for linear matrix hamiltonian systems, Dynam. Systems Appl. 17 (2008), 85–96. (2008) MR2433892

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