2009
DOI: 10.1080/10236190802119903
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On the characterization of rational difference equations

Abstract: We explore the implications of monotonic character for difference equations of order greater than one. Several techniques are developed culminating in the complete characterization of the behaviour of solutions to the k th order rational difference equationAs is customary we assume non-negative parameters and nonnegative initial conditions.

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Cited by 11 publications
(10 citation statements)
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“…[9] when referring to the kth order rational difference equation. Similarly, we shall make extensive use of this notation.…”
Section: Some General Unboundedness Resultsmentioning
confidence: 99%
“…[9] when referring to the kth order rational difference equation. Similarly, we shall make extensive use of this notation.…”
Section: Some General Unboundedness Resultsmentioning
confidence: 99%
“…To be more specific if this occurs, then there is a nontrivial subspace of initial conditions where the solution behaves linearly. In [19] and [20], the author shows that the rational difference equation inheirits trichotomy behavior from the associated linear difference equation in this case. To give a demonstration of this idea consider the most basic case, namely the rational difference equation where there is a single delay present in the numerator and every multiple of that delay is not present in the denominator.…”
Section: A Family Of Periodic Trichotomiesmentioning
confidence: 92%
“…To get around this difficulty we must assume that the matrix, which describes the behavior on the invariant subspace where our equation acts linearly, is Hermitian. Under this assumption monotonicity is replaced by monotonicity in norm, at which point theorems 1 and 2 from [19] are applied. Using this approach the proof goes through in many cases.…”
Section: A Family Of Periodic Trichotomiesmentioning
confidence: 99%
“…These sets are used extensively in [Palladino 2009b] when referring to the k-th order rational difference equation. Similarly we shall make extensive use of this notation.…”
Section: Congruences For Han's Generating Functionmentioning
confidence: 99%