Advances in Difference Equations
Volume 2005 (2005), Issue 2, Pages 193-204
doi:10.1155/ADE.2005.193

Nonoscillatory half-linear difference equations and recessive solutions

Mariella Cecchi,1 Zuzana Došlá,2 and Mauro Marini1

1Department of Electronic and Telecommunications, University of Florence, Via S. Marta 3, Florence 50139, Italy
2Department of Mathematics, Faculty of Science, Masaryk University in Brno, Janáčkovo nám. 2a, Brno 66295, Czech Republic

Received 30 January 2004; Revised 26 May 2004

Copyright © 2005 Mariella Cecchi et al. 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.

Abstract

Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the “smallest solutions in a neighborhood of infinity,” like in the linear case. Other asymptotic properties of recessive and dominant solutions are treated too.