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

Małgorzata Migda, Anna Musielak, and Ewa Schmeidel

 Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, Poznań 60-695, Poland
Received 18 August 2003; Revised 22 October 2003

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.