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

Jones, Austin H. (author)

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