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

Archivum Mathematicum (2018)

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

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topGrigorian, 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

top- 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
- 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
- Erbe, L.H., Kong, Q., Ruan, Sh., Kamenev type theorems for second order matrix differential systems, Proc. Amer. Math. Soc. 117 (4) (1993), 957–962. (1993) MR1154244
- 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
- Grigorian, G.A., 10.3103/S1066369X12110023, Russian Math. (Iz. VUZ) 56 (11) (2012), 17–30. (2012) MR3137099DOI10.3103/S1066369X12110023
- Grigorian, G.A., Global solvability of scalar Riccati equations, Izv. Vyssh. Uchebn. Zaved. Mat. 3 (2015), 35–48. (2015) MR3374339
- Grigorian, G.A., 10.1134/S0012266115030015, Differ. Uravn. 51 (3) (2015), 283–292. (2015) MR3373201DOI10.1134/S0012266115030015
- 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
- Hartman, P., Ordinary differential equations, Classics Appl. Math., SIAM 38 (2002). (2002) Zbl1009.34001MR1929104
- 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
- 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
- Mingarelli, A.B., On a conjecture for oscillation of second order ordinary differential systems, Proc. Amer. Math. Soc. 82 (4), 593–598. MR0614884
- Wang, Q., 10.1007/PL00000448, Arch. Math. (Basel) 76 (2001), 385–390. (2001) MR1824258DOI10.1007/PL00000448
- 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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