Unboundedness results for fourth order rational difference equations

Abstract

We present some new results regarding the boundedness character of the kth order rational difference equation; n [ N:When applied to the general fourth order rational difference equation, these results prove the existence of unbounded solutions for 49 special cases of the fourth order rational difference equation, where the boundedness character has not been established yet. This resolves 49 conjectures posed by E. Camouzis and G. Ladas.

On invariants and forbidden sets

“…Invariants have been used in several cases to provide insight into the behavior of rational difference equations, see [1]- [4], [6]- [10], [12]- [14], [16]- [22], [24], [25], and [38]- [40]. In this article, we introduce six new algebraic invariants for six second order rational difference equations.…”