Geodesic
Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems
Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 289-304
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The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.
The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.
DOI : 10.21136/MB.2020.0149-19
Classification : 34C10
Keywords: Riccati equation; oscillation; non-oscillation; conjoined (prepared, preferred) solution; Liouville's formula 
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Grigorian, Gevorg A. Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems. Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 289-304. doi: 10.21136/MB.2020.0149-19

[1] Al-Dosary, K. I., Abdullah, H. K., Hussein, D.: Short note on oscillation of matrix Hamiltonian systems. Yokohama Math. J. 50 (2003), 23-30. | MR | JFM

[2] Butler, G. J., Erbe, L. H., Mingarelli, A. B.: Riccati techniques and variational principles in oscillation theory for linear systems. Trans. Am. Math. Soc. 303 (1987), 263-282. | DOI | MR | JFM

[3] Byers, R., Harris, B. J., Kwong, M. K.: Weighted means and oscillation conditions for second order matrix differential equations. J. Differ. Equations 61 (1986), 164-177. | DOI | MR | JFM

[4] Chen, S., Zheng, Z.: Oscillation criteria of Yan type for linear Hamiltonian systems. Comput. Math. Appl. 46 (2003), 855-862. | DOI | MR | JFM

[5] Erbe, L. H., Kong, Q., Ruan, S.: Kamenev type theorems for second order matrix differential systems. Proc. Am. Math. Soc. 117 (1993), 957-962. | DOI | MR | JFM

[6] Grigoryan, G. A.: On two comparison tests for second-order linear ordinary differential equations. Differ. Equ. 47 (2011), 1237-1252 translation from Differ. Uravn. 47 2011 1225-1240. | DOI | MR | JFM

[7] Grigoryan, G. A.: Two comparison criteria for scalar Riccati equations with applications. Russ. Math. 56 (2012), 17-30 translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012 2012 20-35. | DOI | MR | JFM

[8] Grigoryan, G. A.: On the stability of systems of two first-order linear ordinary differential equations. Differ. Equ. 51 (2015), 283-292 translation from Differ. Uravn. 51 2015 283-292. | DOI | MR | JFM

[9] Grigorian, G. A.: On one oscillatory criterion for the second order linear ordinary differential equations. Opusc. Math. 36 (2016), 589-601. | DOI | MR | JFM

[10] Grigorian, G. A.: Oscillatory criteria for the systems of two first-order linear differential equations. Rocky Mt. J. Math. 47 (2017), 1497-1524. | DOI | MR | JFM

[11] Grigorian, G. A.: Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations. Arch. Math., Brno 54 (2018), 189-203. | DOI | MR | JFM

[12] Kumary, I. S., Umamaheswaram, S.: Oscillation criteria for linear matrix Hamiltonian systems. J. Differ. Equations 165 (2000), 174-198. | DOI | MR | JFM

[13] Li, L., Meng, F., Zheng, Z.: Oscillation results related to integral averaging technique for linear Hamiltonian systems. Dyn. Syst. Appl. 18 (2009), 725-736. | MR | JFM

[14] Meng, F., Mingarelli, A. B.: Oscillation of linear Hamiltonian systems. Proc. Am. Math. Soc. 131 (2003), 897-904. | DOI | MR | JFM

[15] Mingarelli, A. B.: On a conjecture for oscillation of second order ordinary differential systems. Proc. Am. Math. Soc. 82 (1981), 593-598. | DOI | MR | JFM

[16] Sun, Y. G.: New oscillation criteria for linear matrix Hamiltonian systems. J. Math. Anal. Appl. 279 (2003), 651-658. | DOI | MR | JFM

[17] Wang, Q.: Oscillation criteria for second-order matrix differential systems. Arch. Math. 76 (2001), 385-390. | DOI | MR | JFM

[18] Yang, Q., Mathsen, R., Zhu, S.: Oscillation theorems for self-adjoint matrix Hamiltonian systems. J. Differ. Equations 190 (2003), 306-329. | DOI | MR | JFM

[19] Zheng, Z.: Linear transformation and oscillation criteria for Hamiltonian systems. J. Math. Anal. Appl. 332 (2007), 236-245. | DOI | MR | JFM

[20] Zheng, Z., Zhu, S.: Hartman type oscillation criteria for linear matrix Hamiltonian systems. Dyn. Syst. Appl. 17 (2008), 85-96. | MR | JFM

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