Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 23-36
doi:10.1155/S1687183904308083
On a class of fourth-order nonlinear difference equations
Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, Poznań 60-695, Poland
Received 18 August 2003; Revised 22 October 2003
Copyright © 2004 Małgorzata Migda 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
We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+- and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.