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Publication Date:
February 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2001.135

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Georgian Mathematical Journal

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

Editorial Board Member: 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, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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On Periodic Solutions of Autonomous Difference Equations

A. N. Ronto1 / M. Rontó4 / A. M. Samoilenko2 / S. I. Trofimchuk3

1Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivska St., Kyiv 252601, Ukraine. E-mail: ar@imath.kiev.ua

2Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivska St., Kyiv 252601, Ukraine. E-mail: sam@imath.kiev.ua

3Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivska St., Kyiv 252601, Ukraine. E-mail: trofimch@imath.kiev.ua

4Institute of Mathematics, University of Miskolc, H-3515 Miskolc–Egyetemváros, Hungary. E-mail: matronto@gold.uni-miskolc.hu

Citation Information: Georgian Mathematical Journal. Volume 8, Issue 1, Pages 135–164, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2001.135, February 2010

Publication History:
Received:
2000-03-20
Published Online:
2010-02-23

Abstract

We establish conditions necessary for the existence of non-constant periodic solutions of non-linear autonomous difference equations with Lipschitzian right-hand sides.

Key words and phrases:: Periodic solution; autonomous system; difference equation; cone; partially ordered space; fixed point

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