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ON THIRD-ORDER LINEAR DIFFERENCE EQUATIONS INVOLVING QUASI-DIFFERENCES ˇ ´ ˇ ZUZANA DOSLA AND

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ON THIRD-ORDER LINEAR DIFFERENCE EQUATIONS INVOLVING QUASI-DIFFERENCESˇ ´ ˇ ZUZANA DOSLA AND ALES KOBZA Received 30 June 2004; Revised 20 September 2004; Accepted 12 October 2004We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of both equations. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Introduction Consider the third-order linear difference equation Δ pn Δ rn Δxn and its adjoint equation Δ rn+1 Δ pn Δun− qn+1 un+2 = 0,+ qn xn+1 = 0(E)(EA )where Δ is the forward difference...
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ON THIRD-ORDER LINEAR DIFFERENCE EQUATIONS INVOLVING QUASI-DIFFERENCES ˇ ´ ˇ ZUZANA DOSLA AND

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