Glasnik Matematicki, Vol. 53, No. 1 (2018), 123-141.

EXISTENCE AND BOUNDEDNESS OF SOLUTIONS FOR SYSTEMS OF DIFFERENCE EQUATIONS WITH INFINITE DELAY

Juan J. Nieto, Abdelghani Ouahab and Mohammed A. Slimani

Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain
e-mail: juanjose.nieto.roig@usc.es

Laboratory of Mathematics, University of Sidi Bel-Abbès, P.O. Box 89, 22000 Sidi Bel-Abbès, Algeria
e-mail: agh_ouahab@yahoo.fr

Laboratory of Mathematics, University of Sidi Bel-Abbès, P.O. Box 89, 22000 Sidi Bel-Abbès, Algeria
e-mail: sedikslimani@yahoo.fr

Abstract.   In this work we first establish some existence results followed by boundedness behavior and asymptotic behavior of solutions for systems of difference equations with infinite delay. Our approach is based on a Perov fixed point theorem in vector metric space. We apply our results to a system of Volterra difference equations.

2010 Mathematics Subject Classification.   34K45, 34A60.

Key words and phrases.   Difference equations, fixed point, infinite delay, boundedness, asymptotic behavior, matrix convergent to zero.

Full text (PDF) (free access)

DOI: 10.3336/gm.53.1.09

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