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 Cecchi1
, Zuzana Došlá2
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, Janá {c}kovo nám. 2a, Brno 66295, Czech Republic
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.