{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/14684"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/14684","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Some New Results on Composition-Delay Equations with Asymptotically Periodic Solutions","abstract":"The purpose of this thesis is to convey several new results in the field of piecewise difference equations, paying particular attention to higher order equations with asymptotically periodic solutions. A study of solutions to the equation $$y_n = \\min \\{ y_{n-k_1}-y_{n-m_1} , y_{n-k_2}-y_{n-m_2} \\}$$ is presented. Related results are then obtained for a class of difference equations satisfying certain symmetry and monotonicity conditions. In particular we consider equations of the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2} ) \\}, $$ where $f(u,v) = h(u,v)/v$ for $h$ symmetric in $u$ and $v,$ and $f$ satisfies monotonicity conditions. The results are then extended to the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2}),\\dots ,f( y_{n-k_L} , y_{n-m_L} ) \\} .$$","abstract_html":"The purpose of this thesis is to convey several new results in the field of piecewise difference equations, paying particular attention to higher order equations with asymptotically periodic solutions. A study of solutions to the equation $<span class=\"etd-inline-math\">y<sub>n</sub> = \\min \\{ y<sub>n-k<sub>1</sub></sub>-y<sub>n-m<sub>1</sub></sub> , y<sub>n-k<sub>2</sub></sub>-y<sub>n-m<sub>2</sub></sub> \\}</span>$ is presented. Related results are then obtained for a class of difference equations satisfying certain symmetry and monotonicity conditions. In particular we consider equations of the form $<span class=\"etd-inline-math\"> y<sub>n</sub> = \\min \\{ f(y<sub>n-k<sub>1</sub></sub>,y<sub>n-m<sub>1</sub></sub> ),f( y<sub>n-k<sub>2</sub></sub> , y<sub>n-m<sub>2</sub></sub> ) \\}, </span>$ where $f(u,v) = h(u,v)/v$ for $h$ symmetric in $u$ and $v,$ and $f$ satisfies monotonicity conditions. The results are then extended to the form $<span class=\"etd-inline-math\"> y<sub>n</sub> = \\min \\{ f(y<sub>n-k<sub>1</sub></sub>,y<sub>n-m<sub>1</sub></sub> ),f( y<sub>n-k<sub>2</sub></sub> , y<sub>n-m<sub>2</sub></sub>),\\dots ,f( y<sub>n-k<sub>L</sub></sub> , y<sub>n-m<sub>L</sub></sub> ) \\} .</span>$","abstract_has_math":true,"creators":["Guy, Richard"],"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":2009,"date_issued":"2009-05-07T14:36:52Z","date_published":"2009-05-07T14:36:52Z","updated_at":"2026-07-27T22:00:55Z","subjects":["Discrete Mathematics"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/14684","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Guy, Richard"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2009-05-07T14:36:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-05-07T14:36:52Z"]},{"key":"dc:date.issued","label":"Date","values":["2009-05-07T14:36:52Z"]},{"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":["Discrete Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/14684"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to convey several new results in the field of piecewise difference equations, paying particular attention to higher order equations with asymptotically periodic solutions. A study of solutions to the equation $$y_n = \\min \\{ y_{n-k_1}-y_{n-m_1} , y_{n-k_2}-y_{n-m_2} \\}$$ is presented. Related results are then obtained for a class of difference equations satisfying certain symmetry and monotonicity conditions. In particular we consider equations of the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2} ) \\}, $$ where $f(u,v) = h(u,v)/v$ for $h$ symmetric in $u$ and $v,$ and $f$ satisfies monotonicity conditions. The results are then extended to the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2}),\\dots ,f( y_{n-k_L} , y_{n-m_L} ) \\} .$$"]},{"key":"dc:title","label":"Title","values":["Some New Results on Composition-Delay Equations with Asymptotically Periodic Solutions"]}]}],"canonical_facts":{"dc:creator":["Guy, Richard"],"dc:date.accessioned":["2009-05-07T14:36:52Z"],"dc:date.available":["2009-05-07T14:36:52Z"],"dc:date.issued":["2009-05-07T14:36:52Z"],"dc:description.abstract":["The purpose of this thesis is to convey several new results in the field of piecewise difference equations, paying particular attention to higher order equations with asymptotically periodic solutions. A study of solutions to the equation $$y_n = \\min \\{ y_{n-k_1}-y_{n-m_1} , y_{n-k_2}-y_{n-m_2} \\}$$ is presented. Related results are then obtained for a class of difference equations satisfying certain symmetry and monotonicity conditions. In particular we consider equations of the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2} ) \\}, $$ where $f(u,v) = h(u,v)/v$ for $h$ symmetric in $u$ and $v,$ and $f$ satisfies monotonicity conditions. The results are then extended to the form $$ y_n = \\min \\{ f(y_{n-k_1},y_{n-m_1} ),f( y_{n-k_2} , y_{n-m_2}),\\dots ,f( y_{n-k_L} , y_{n-m_L} ) \\} .$$"],"dc:identifier.uri":["http://hdl.handle.net/10339/14684"],"dc:language.iso":["en_US"],"dc:publisher":["Wake Forest University"],"dc:subject":["Discrete Mathematics"],"dc:title":["Some New Results on Composition-Delay Equations with Asymptotically Periodic Solutions"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:00:55Z"}