{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/4185"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/4185","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations.","abstract":"For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\\geq 4$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_m)-\\sum_{i=3}^{m-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_m<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is proved that, for all $3\\leq k \\leq m$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_k)-\\sum_{i=3}^{k-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_k<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is then shown that solutions do indeed exist.","abstract_html":"For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\\geq 4$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_m)-\\sum_{i=3}^{m-1} y(x_{i})=y_3,\\] a<x1<x2<\\cdots<xm<b, and y1,y2,y3\\in\\mathbb{R}, are unique when they exist. It is proved that, for all $3\\leq k \\leq m$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_k)-\\sum_{i=3}^{k-1} y(x_{i})=y_3,\\] a<x1<x2<\\cdots<xk<b, and y1,y2,y3\\in\\mathbb{R}, are unique when they exist. It is then shown that solutions do indeed exist.","abstract_has_math":true,"creators":["Gray, Michael Jeffery."],"institution":"Baylor University.","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Henderson, Johnny."],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-07","date_published":"2006-07","updated_at":"2026-07-24T01:07:58Z","subjects":["Boundary value problems -- Research.","Differential equations -- Research."],"languages":["en"],"rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2104/4185","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Henderson, Johnny."]},{"key":"dc:creator","label":"Author","values":["Gray, Michael Jeffery."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2006-07-29T16:00:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2006-07-29T16:00:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2006-07"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Baylor University."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Boundary value problems -- Research.","Differential equations -- Research."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2104/4185"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\\geq 4$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_m)-\\sum_{i=3}^{m-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_m<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is proved that, for all $3\\leq k \\leq m$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_k)-\\sum_{i=3}^{k-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_k<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is then shown that solutions do indeed exist."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations."]}]}],"canonical_facts":{"dc:contributor.advisor":["Henderson, Johnny."],"dc:creator":["Gray, Michael Jeffery."],"dc:date.accessioned":["2006-07-29T16:00:19Z"],"dc:date.available":["2006-07-29T16:00:19Z"],"dc:date.issued":["2006-07"],"dc:description.abstract":["For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\\geq 4$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_m)-\\sum_{i=3}^{m-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_m<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is proved that, for all $3\\leq k \\leq m$, solutions of nonlocal boundary value problems satisfying \\[y(x_1)=y_1,\\ y(x_2)=y_2,\\] \\[y(x_k)-\\sum_{i=3}^{k-1} y(x_{i})=y_3,\\] $a<x_1<x_2<\\cdots<x_k<b$, and $y_1,y_2,y_3\\in\\mathbb{R}$, are unique when they exist. It is then shown that solutions do indeed exist."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/4185"],"dc:language.iso":["en"],"dc:rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"dc:subject":["Boundary value problems -- Research.","Differential equations -- Research."],"dc:title":["Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:07:58Z"}