{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/33456"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/33456","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials","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).","abstract_html":"This thesis studies the behavior of positive solutions of the recursive equation <span class=\"etd-inline-math\">y<sub>n</sub>=\\left(\\frac{e<sub>i,k</sub>}{e<sub>j,k</sub>}\\right)(y<sub>n-t<sub>1</sub></sub>,y<sub>n-t<sub>2</sub></sub>,\\dots,y<sub>n-t<sub>k</sub></sub>), 0\\leq i, j \\leq k</span>, where <span class=\"etd-inline-math\">e<sub>m,k</sub></span> is the <span class=\"etd-inline-math\">m<sup>th</sup></span> elementary symmetric polynomial on $k$ variables, <span class=\"etd-inline-math\">t<sub>l</sub> \\geq 1</span> for $1\\leq l\\leq k$, <span class=\"etd-inline-math\">\\gcd(t<sub>1</sub>,t<sub>2</sub>,\\dots,t<sub>k</sub>)=1</span> and <span class=\"etd-inline-math\">y<sub>-s</sub>,y<sub>-s+1</sub>,\\ldots, y<sub>-1</sub> \\in \\mathbb{R<sup>+</sup>}</span>, with <span class=\"etd-inline-math\">s=\\max\\{t<sub>1</sub>,t<sub>2</sub>,\\dots,t<sub>k</sub>\\}</span>. A variant of Newton&#x27;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 \\&amp; Hall/CRC Press, Boca Raton (2004).","abstract_has_math":true,"creators":["Jones, Austin H."],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-27T22:01:14Z","subjects":["difference equation"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/33456","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jones, Austin H."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-07-14T20:35:35Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["difference equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/33456"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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)."]},{"key":"dc:title","label":"Title","values":["Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials"]}]}],"canonical_facts":{"dc:creator":["Jones, Austin H."],"dc:date.accessioned":["2011-07-14T20:35:35Z"],"dc:date.issued":["2011"],"dc:description.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)."],"dc:identifier.uri":["http://hdl.handle.net/10339/33456"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["difference equation"],"dc:title":["Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:14Z"}