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
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.