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

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-t1,y_n-t2,\dots,y_n-tk), 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(t₁,t₂,\dots,t_k)=1 and y_-s,y_-s+1,\ldots, y_-1 \in \mathbb{R⁺}, with s=\max\{t₁,t₂,\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).

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2011

Author dc:creator

• Jones, Austin H.

• difference equation

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/33456

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/33456