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Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations

Published online by Cambridge University Press:  20 November 2018

Lynn H. Erbe  and
Pengxiang Yan
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Abstract

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We consider the self-adjoint second-order scalar difference equation (1) Δ(rnΔxn) +pnXn+1 = 0 and the matrix system (2) Δ(RnΔXn) + PnXn+1 = 0, where are seQuences of real numbers (d x d Hermitian matrices) with rn > 0(Rn > 0). The oscillation and nonoscillation criteria for solutions of (1) and (2), obtained in [3, 4, 10], are extended to a much wider class of equations by Riccati and averaging techniques.

Keywords

39A10.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 61 - 69
Copyright
Copyright © Canadian Mathematical Society 1992

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