On the oscillation of a third order rational difference equation

In this paper, we discuss the global asymptotic stability of all solutions of the difference equation xn+1=Axn-2B+Cxnxn-1xn-2,n=0,1,… where A,B,C are positive real numbers and the initial conditions x-2,x-1,x0 are real numbers. Although we have an explicit formula for the solutions of that equation,...

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Bibliographic Details
Published inJournal of the Egyptian Mathematical Society Vol. 23; no. 1; pp. 62 - 66
Main Author Abo-Zeid, R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2015
Subjects
Difference equation
Locally asymptotically stable
Oscillation
Periodic solution
39A20
39A30
39A21
39A23
Oscillation
Difference equation
Periodic solution
Locally asymptotically stable
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Summary:In this paper, we discuss the global asymptotic stability of all solutions of the difference equation xn+1=Axn-2B+Cxnxn-1xn-2,n=0,1,… where A,B,C are positive real numbers and the initial conditions x-2,x-1,x0 are real numbers. Although we have an explicit formula for the solutions of that equation, the oscillation character is worth to be discussed.
ISSN:1110-256X
2090-9128
DOI:10.1016/j.joems.2014.03.001