{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/5026"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/5026","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"A functional approach to positive solutions of boundary value problems.","abstract":"We apply a well-known fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing second order problems having left and right focal boundary conditions. Via an appropriate substitution, associated third, fourth, and nth order problems are resolved. Our main result centers on the nth order equation y(n) + f(y(t)) = 0, t [is an element of] [0, 1], (1) having boundary conditions, y(ri−1)(0) = 0, 1 < i < k, (2) y(sj−1)(1) = 0, 1 < j < n − k, (3) where {s1, · · · , sn−k} and {r1, · · · , rk} form a partition of {1, · · · , n} such that r1 < · · · < rk, s1 < · · · < sn−k, and {rk−1 · · · rk} [is not equal to] {n − 1, n} and {sn−k−1, sn−k} [is not equal to] {n − 1, n}. Under these assumptions we show that the differential equation (1) with boundary conditions (2) and (3) has a positive solution for all n [is greater than or equal to] 2.","abstract_html":"We apply a well-known fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing second order problems having left and right focal boundary conditions. Via an appropriate substitution, associated third, fourth, and nth order problems are resolved. Our main result centers on the nth order equation y(n) + f(y(t)) = 0, t [is an element of] [0, 1], (1) having boundary conditions, y(ri−1)(0) = 0, 1 < i < k, (2) y(sj−1)(1) = 0, 1 < j < n − k, (3) where {s1, · · · , sn−k} and {r1, · · · , rk} form a partition of {1, · · · , n} such that r1 < · · · < rk, s1 < · · · < sn−k, and {rk−1 · · · rk} [is not equal to] {n − 1, n} and {sn−k−1, sn−k} [is not equal to] {n − 1, n}. Under these assumptions we show that the differential equation (1) with boundary conditions (2) and (3) has a positive solution for all n [is greater than or equal to] 2.","abstract_has_math":false,"creators":["Ehrke, John E."],"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":2007,"date_issued":"2007-05","date_published":"2007-05","updated_at":"2026-07-24T01:07:56Z","subjects":["Boundary value problems.","Fixed point theory.","Functionals."],"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/2104/5026","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":["Ehrke, John E."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2007-05-23T19:30:41Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2007-05-23T19:30:41Z"]},{"key":"dc:date.issued","label":"Date","values":["2007-05"]},{"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.","Fixed point theory.","Functionals."]}]},{"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/2104/5026"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We apply a well-known fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing second order problems having left and right focal boundary conditions. Via an appropriate substitution, associated third, fourth, and nth order problems are resolved. Our main result centers on the nth order equation y(n) + f(y(t)) = 0, t [is an element of] [0, 1], (1) having boundary conditions, y(ri−1)(0) = 0, 1 < i < k, (2) y(sj−1)(1) = 0, 1 < j < n − k, (3) where {s1, · · · , sn−k} and {r1, · · · , rk} form a partition of {1, · · · , n} such that r1 < · · · < rk, s1 < · · · < sn−k, and {rk−1 · · · rk} [is not equal to] {n − 1, n} and {sn−k−1, sn−k} [is not equal to] {n − 1, n}. Under these assumptions we show that the differential equation (1) with boundary conditions (2) and (3) has a positive solution for all n [is greater than or equal to] 2."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A functional approach to positive solutions of boundary value problems."]}]}],"canonical_facts":{"dc:contributor.advisor":["Henderson, Johnny."],"dc:creator":["Ehrke, John E."],"dc:date.accessioned":["2007-05-23T19:30:41Z"],"dc:date.available":["2007-05-23T19:30:41Z"],"dc:date.issued":["2007-05"],"dc:description.abstract":["We apply a well-known fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing second order problems having left and right focal boundary conditions. Via an appropriate substitution, associated third, fourth, and nth order problems are resolved. Our main result centers on the nth order equation y(n) + f(y(t)) = 0, t [is an element of] [0, 1], (1) having boundary conditions, y(ri−1)(0) = 0, 1 < i < k, (2) y(sj−1)(1) = 0, 1 < j < n − k, (3) where {s1, · · · , sn−k} and {r1, · · · , rk} form a partition of {1, · · · , n} such that r1 < · · · < rk, s1 < · · · < sn−k, and {rk−1 · · · rk} [is not equal to] {n − 1, n} and {sn−k−1, sn−k} [is not equal to] {n − 1, n}. Under these assumptions we show that the differential equation (1) with boundary conditions (2) and (3) has a positive solution for all n [is greater than or equal to] 2."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/5026"],"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.","Fixed point theory.","Functionals."],"dc:title":["A functional approach to positive solutions of boundary value problems."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:07:56Z"}