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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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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


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


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


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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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