OSCILLATION THEOREM FOR SECOND-ORDER DIFFERENCE EQUATIONS

OSCILLATION THEOREM FOR SECOND-ORDER DIFFERENCE EQUATIONS

Sufficient and necessary conditions are established for the secondorder difference equations $\Delta \left( {{r_{n - 1}}\Delta {x_{n - 1}}} \right) + {p_n}x_n^\gamma = 0,n = 1,2,...$ where γ is the quotient of odd positive integers. Our results extend the well known oscillation theorem which was pro...

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Veröffentlicht in:Taiwanese journal of mathematics 2008-06, Vol.12 (3), p.623-633
Hauptverfasser: Cheng, Jinfa, 程金發, Chu, Yuming, 褚玉明
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Sprache:eng
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Difference equations
Differential equations
Integers
Mathematical theorems
Necessary conditions
Sufficient conditions
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container_issue 3
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container_title Taiwanese journal of mathematics
container_volume 12
creator Cheng, Jinfa
程金發
Chu, Yuming
褚玉明
description Sufficient and necessary conditions are established for the secondorder difference equations $\Delta \left( {{r_{n - 1}}\Delta {x_{n - 1}}} \right) + {p_n}x_n^\gamma = 0,n = 1,2,...$ where γ is the quotient of odd positive integers. Our results extend the well known oscillation theorem which was proved in [1,JMAA,91:9-29,1983], and answer an open problem in [2] when rn = 1, γ = 1.
doi_str_mv 10.11650/twjm/1500602425
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source JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Project Euclid Open Access; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete
subjects Difference equations
Differential equations
Integers
Mathematical theorems
Necessary conditions
Sufficient conditions
title OSCILLATION THEOREM FOR SECOND-ORDER DIFFERENCE EQUATIONS
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