Previous |  Up |  Next

Article

Title: Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations (English)
Author: Grigorian, Gevorg Avagovich
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 4
Year: 2018
Pages: 189-203
Summary lang: English
.
Category: math
.
Summary: 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. (English)
Keyword: Riccati equation
Keyword: oscillation
Keyword: non oscillation
Keyword: prepared (preferred) solution
Keyword: Liouville’s formula
MSC: 34C10
idZBL: Zbl 06997350
idMR: MR3887360
DOI: 10.5817/AM2018-4-189
.
Date available: 2018-12-06T16:04:36Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147496
.
Reference: [1] Butler, G.J., Erbe, L.H., Mingarelli, A.B.: Riccati techniques and variational principles in oscillation theory for linear systems.Trans. Amer. Math. Soc. 303 (1) (1987), 263–282. MR 0896022, 10.1090/S0002-9947-1987-0896022-5
Reference: [2] Byers, R., Harris, B.J., Kwong, M.K.: Weighted means and oscillation conditions for second order matrix differential equations.J. Differential Equations 61 (1986), 164–177. MR 0823400, 10.1016/0022-0396(86)90117-8
Reference: [3] 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. MR 1154244
Reference: [4] Grigorian, G.A.: On two comparison tests for second-order linear ordinary differential equations.Differ. Uravn. 47 (2011), 1225–1240, translation in Differential Equations 47 (2011), no. 9 1237–1252. MR 2918496, 10.1134/S0012266111090023
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. Vyssh. Uchebn. Zaved. Mat. 3 (2015), 35–48. MR 3374339
Reference: [7] Grigorian, G.A.: On the stability of systems of two first-order linear ordinary differential equations.Differ. Uravn. 51 (3) (2015), 283–292. MR 3373201, 10.1134/S0012266115030015
Reference: [8] Grigorian, G.A.: On one oscillatory criterion for the second order linear ordinary differential equations.Opuscula Math. 36 (5) (2016), 589–601, http://dx.doi.org/10.7494/OpMath.2016.36.5.589. MR 3520801, 10.7494/OpMath.2016.36.5.589
Reference: [9] Hartman, P.: Ordinary differential equations.Classics Appl. Math., SIAM 38 (2002). Zbl 1009.34001, MR 1929104
Reference: [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. MR 2562259
Reference: [11] Meng, F., Mingarelli, A.B.: Oscillation of linear hamiltonian systems.Proc. Amer. Math. Soc. 131 (3) (2002), 897–904. MR 1937428, 10.1090/S0002-9939-02-06614-5
Reference: [12] Mingarelli, A.B.: On a conjecture for oscillation of second order ordinary differential systems.Proc. Amer. Math. Soc. 82 (4), 593–598. MR 0614884
Reference: [13] Wang, Q.: Oscillation criteria for second order matrix differential systems.Arch. Math. (Basel) 76 (2001), 385–390. MR 1824258, 10.1007/PL00000448
Reference: [14] Zhung, Z., Zhu, S.: Hartman type oscillation criteria for linear matrix hamiltonian systems.Dynam. Systems Appl. 17 (2008), 85–96. MR 2433892
.

Files

Files Size Format View
ArchMathRetro_054-2018-4_1.pdf 536.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo