Authors: Stević, Stevo 
Diblík, Josef
Iričanin, Bratislav
Šmarda, Zdeněk
Title: Solvability of nonlinear difference equations of fourth order
Journal: Electronic Journal of Differential Equations
Volume: 2014
Issue Date: 22-Dec-2014
Rank: M22
URL: https://ejde.math.txstate.edu/Volumes/2014/264/stevic.pdf
Abstract: 
In this article we show the existence of solutions to the nonlinear difference equation (Formula Presented.) where the sequences (an)nєN0 and (bn) nєN0, and initial the values x-j, j = 1, 4, are real numbers. Also we find the set of initial values for which solutions are undefinable when an ≠0 and bn ≠0 for every n є ℕo. When these two sequences are constant, we describe the long-term behavior of the solutions in detail.
Keywords: Long-term behavior of solutions | Solution to difference equation | Undefinable solutions
Publisher: Texas State University - San Marcos
Project: Operational Programme Research and Development for Innovations, No. CZ.1.05/2.1.00/03.0097 (AdMaS).
Brno University of Technology, Project no. FEKT-S-14-2200
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