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

## Electronic Theses and Dissertations

### Item Details

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)
10000-01-01 (liftdate)
embargo
forever (terms)
identifier
http://hdl.handle.net/10339/33456 (uri)
language
en (iso)
publisher
Wake Forest University
title
Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials
type
Thesis