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oai:null:10339/334562026-09-02T15:22:08Zcom_10339_14934col_10339_38132

Jones, Austin H. 2011-07-14T20:35:35Z 2011 https://wakespace.lib.wfu.edu/handle/10339/33456 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). en Wake Forest University difference equation elementary symmetric polynomial recursive equation Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials Thesis Berenhaut, Kenneth S Rouse, Jeremy A Mathematics forever 10000-01-01 restricted