On some difference equations with exponential nonlinearity

Eugenia N. Petropoulou

doi:10.3934/dcdsb.2017098

Article Contents

2017, Volume 22, Issue 7: 2587-2594. Doi: 10.3934/dcdsb.2017098

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On some difference equations with exponential nonlinearity

Eugenia N. Petropoulou

Department of Civil Engineering, University of Patras, 26500 Patras, Greece

Received: June 30, 2016

Revised: November 30, 2016

Published: October 2017

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Abstract

The problem of the existence of complex $\ell_1$ solutions of two difference equations with exponential nonlinearity is studied, one of which is nonautonomous. As a consequence, several information are obtained regarding the asymptotic stability of their equilibrium points, as well as the corresponding generating function and $z-$ transform of their solutions. The results, which are obtained using a general theorem based on a functional-analytic technique, provide also a rough estimate of the region of attraction of each equilibrium point for the autonomous case. When restricted to real solutions, the results are compared with other recently published results.

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Mathematics Subject Classification: Primary:39A30, 39A22;Secondary:39A45.

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