Weighted means and oscillation conditions for second order matrix differential equations

Byers, Ralph; Harris, Bernard; Kam, Man Kwong

doi:10.1016/0022-0396(86)90117-8

Cited by 67 publications

(44 citation statements)

References 7 publications

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“…This conjecture was proved by Kwong and Kaper [10] in the two-dimensional case, and by Byers et al [4] in the n-dimensional case. Here we list the main results of [6] as follows:…”

Section: = A(t)x + B(t)y Y = C(t)x −mentioning

confidence: 71%

Oscillation of linear Hamiltonian systems

Meng

Mingarelli

2002

Proc. Amer. Math. Soc.

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“…This conjecture was proved by Kwong and Kaper [10] in the two-dimensional case, and by Byers et al [4] in the n-dimensional case. Here we list the main results of [6] as follows:…”

Section: = A(t)x + B(t)y Y = C(t)x −mentioning

confidence: 71%

Oscillation of linear Hamiltonian systems

Meng

Mingarelli

2002

Proc. Amer. Math. Soc.

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“…This conjecture was partially proved by several authors and finally settled by Byers, Harris and Kwong [3]. Coles [4 , 5] extended this result by applying the weighted average method.…”

Section: Zhaowen Zheng and Jingzhao Liumentioning

confidence: 91%

Interval oscillation criteria for matrix differential systems with damping

Liu

Meng

2008

Applied Mathematics and Computation

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“…Finally, it has recently been shown by Byers, Harris and Kwong [6] that (1.10) lim Ai í / Q(s)ds) = +oo without any additional conditions, is an oscillation criterion for (1.1). This gives, therefore, the desired systems analogue of the Fite-Wintner condition.…”

Section: 3) Y*(t)y'(t) -Y*'(t)y(t) = 0 Ie[o+oo)mentioning

confidence: 94%

“…As was mentioned in §1, the systems analogue of the Fite-Wintner theorem has been recently obtained [6]. That a complete analogue of the corresponding scalar oscillation theorem employing only the behavior of Ai is not always available for systems will be shown for the Wintner criterion (2.7) in §4.…”

Section: 3) Y*(t)y'(t) -Y*'(t)y(t) = 0 Ie[o+oo)mentioning

confidence: 97%

Riccati techniques and variational principles in oscillation theory for linear systems

Butler¹,

Erbe²,

Mingarelli³

1987

Trans. Amer. Math. Soc.

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ABSTRACT. We consider the seond order differential system (1) Y" + Q(i)Y = 0, where Q, Y are nxn matrices with Q = Q(t) a continuous symmetric matrixvalued function, t € [a,+00).We obtain a number of sufficient conditions in order that all prepared solutions Y(t) of (1) are oscillatory. Two approaches are considered, one based on Riccati techniques and the other on variational techniques, and involve assumptions on the behavior of the eigenvalues of Q{t) (or of its integral). These results extend some well-known averaging techniques for scalar equations to system (1).

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Weighted means and oscillation conditions for second order matrix differential equations

Cited by 67 publications

References 7 publications

Oscillation of linear Hamiltonian systems

Oscillation of linear Hamiltonian systems

Interval oscillation criteria for matrix differential systems with damping

Riccati techniques and variational principles in oscillation theory for linear systems

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