Advances in Difference Equations
Volume 2010 (2010), Article ID 673761, 16 pages
Research Article

Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient

1Department of Electronics and Telecommunications, University of Florence, 50139 Florence, Italy
2Institute of Mathematics, Academy of Sciences CR, Žižkova 22, 61662 Brno, Czech Republic

Received 15 June 2010; Accepted 25 October 2010

Academic Editor: E. Thandapani

Copyright © 2010 Serena Matucci and Pavel Řehák. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Necessary and sufficient conditions for regular or slow variation of all positive solutions of a second-order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called 𝕄 -classification are also analyzed and a generalization of the results to the half-linear case completes the paper.