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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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1572-9176
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On the solutions of a higher order difference equation

Raafat Abo-Zeid
  • Corresponding author
  • Department of Basic Science, The Higher Institute for Engineering & Technology, Al-Obour, Cairo, Egypt
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Published Online: 2018-02-20 | DOI: https://doi.org/10.1515/gmj-2018-0008

Abstract

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation

xn+1=axnxn-kbxn-cxn-k-1,n=0,1,,

where a,b,c are positive real numbers and the initial conditions x-k-1,x-k,,x-1,x0 are real numbers. We show that when a=b=c, the behavior of the solutions depends on whether k is even or odd.

Keywords: Difference equation; forbidden set; periodic solution; convergence; unbounded solution

MSC 2010: 39A10; 39A20

References

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About the article

Received: 2015-08-31

Accepted: 2016-05-25

Published Online: 2018-02-20


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0008.

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