{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1859"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1859","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Nontrivial solutions for nonlinear discrete boundary value problems of the fourth order","abstract":"We study the existence of multiple nontrivial solutions for two nonlinear fourth order discrete boundary value problems. We first establish criteria for the existence of at least two nontrivial solutions of the problems and obtain conditions to guarantee that the two solutions are sign-changing. Under some appropriate assumptions, we further prove that the problems have at least three nontrivial solutions, which are respectively positive, negative, and sign-changing. We include two examples to illustrate the applicability of our results. Our theorems are proved by employing variational approaches, combined with the classic mountain pass lemma and a result from the theory of invariant sets of descending flow.","abstract_html":"We study the existence of multiple nontrivial solutions for two nonlinear fourth order discrete boundary value problems. We first establish criteria for the existence of at least two nontrivial solutions of the problems and obtain conditions to guarantee that the two solutions are sign-changing. Under some appropriate assumptions, we further prove that the problems have at least three nontrivial solutions, which are respectively positive, negative, and sign-changing. We include two examples to illustrate the applicability of our results. Our theorems are proved by employing variational approaches, combined with the classic mountain pass lemma and a result from the theory of invariant sets of descending flow.","abstract_has_math":false,"creators":["Layne, Danielle"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kong, Lingju","Graef, John R., 1942-; Nichols, Roger; Want, Jin","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:59Z","subjects":["Calculus of variations","Nonlinear boundary value problems"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/705","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kong, Lingju","Graef, John R., 1942-; Nichols, Roger; Want, Jin","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Layne, Danielle"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-05-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Calculus of variations","Nonlinear boundary value problems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/705"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["We study the existence of multiple nontrivial solutions for two nonlinear fourth order discrete boundary value problems. We first establish criteria for the existence of at least two nontrivial solutions of the problems and obtain conditions to guarantee that the two solutions are sign-changing. Under some appropriate assumptions, we further prove that the problems have at least three nontrivial solutions, which are respectively positive, negative, and sign-changing. We include two examples to illustrate the applicability of our results. Our theorems are proved by employing variational approaches, combined with the classic mountain pass lemma and a result from the theory of invariant sets of descending flow."]},{"key":"dc:title","label":"Title","values":["Nontrivial solutions for nonlinear discrete boundary value problems of the fourth order"]}]}],"canonical_facts":{"dc:contributor":["Kong, Lingju","Graef, John R., 1942-; Nichols, Roger; Want, Jin","College of Arts and Sciences"],"dc:creator":["Layne, Danielle"],"dc:date":["2021-05-01T07:00:00Z"],"dc:description":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."],"dc:description.abstract":["We study the existence of multiple nontrivial solutions for two nonlinear fourth order discrete boundary value problems. We first establish criteria for the existence of at least two nontrivial solutions of the problems and obtain conditions to guarantee that the two solutions are sign-changing. Under some appropriate assumptions, we further prove that the problems have at least three nontrivial solutions, which are respectively positive, negative, and sign-changing. We include two examples to illustrate the applicability of our results. Our theorems are proved by employing variational approaches, combined with the classic mountain pass lemma and a result from the theory of invariant sets of descending flow."],"dc:identifier":["https://scholar.utc.edu/theses/705"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Calculus of variations","Nonlinear boundary value problems"],"dc:title":["Nontrivial solutions for nonlinear discrete boundary value problems of the fourth order"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:46:59Z"}