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Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials

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title
Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials
author
Jones, Austin H.
abstract
This thesis studies the behavior of positive solutions of the recursive equation $y_n=\left(\frac{e_{i,k}}{e_{j,k}}\right)(y_{n-t_1},y_{n-t_2},\dots,y_{n-t_k}), 0\leq i, j \leq k$, where $e_{m,k}$ is the $m^{th}$ elementary symmetric polynomial on $k$ variables, $t_l \geq 1$ for $1\leq l\leq k$, $\gcd(t_1,t_2,\dots,t_k)=1$ and $y_{-s},y_{-s+1},\ldots, y_{-1} \in \mathbb{R^+}$, with $s=\max\{t_1,t_2,\dots,t_k\}$. A variant of Newton's inequalities is employed. Included amongst the results is a generalization of a particular case of Theorem 4.11 in E. A. Grove and G. Ladas, {\em Periodicities in Nonlinear Difference Equations}, Chapman \& Hall/CRC Press, Boca Raton (2004).
subject
difference equation
elementary symmetric polynomial
recursive equation
contributor
Berenhaut, Kenneth S (committee chair)
Rouse, Jeremy A (committee member)
date
2011-07-14T20:35:35Z (accessioned)
2011 (issued)
degree
Mathematics (discipline)
embargo
forever (terms)
10000-01-01 (liftdate)
identifier
http://hdl.handle.net/10339/33456 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

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