{"id":{"repo_id":"wku-diss","oai_identifier":"oai:digitalcommons.wku.edu:theses-1060"},"canonical_url":"https://search.dev.ndltd.org/etd/wku-diss/oai:digitalcommons.wku.edu:theses-1060","repository":{"repo_id":"wku-diss","name":"Western Kentucky University","base_url":"https://digitalcommons.wku.edu/do/oai/"},"display":{"title":"Qualitative Behavior of Solutions to Differential Equations in <i>R</i><sup><em>n</em></sup> and in Hilbert Space","abstract":"The qualitative behavior of solutions of differential equations mainly addresses the various questions arising in the study of the long run behavior of solutions. The contents of this thesis are related to three of the major problems of the qualitative theory, namely the stability, the boundedness and the periodicity of the solution. Learning the qualitative behavior of such solutions is crucial part of the theory of differential equations. It is important to know if a solution is bounded or unbounded or if a solution is stable. Moreover, the periodicity of a solution is also of great significance for practical purposes.","abstract_html":"The qualitative behavior of solutions of differential equations mainly addresses the various questions arising in the study of the long run behavior of solutions. The contents of this thesis are related to three of the major problems of the qualitative theory, namely the stability, the boundedness and the periodicity of the solution. Learning the qualitative behavior of such solutions is crucial part of the theory of differential equations. It is important to know if a solution is bounded or unbounded or if a solution is stable. Moreover, the periodicity of a solution is also of great significance for practical purposes.","abstract_has_math":false,"creators":["Dong, Qian"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics and Computer Science","degree_department":null,"school":null,"contributors":["Dr. Lan Nguyen (Director), Dr. John Spraker,Dr. Di Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-05-01T07:00:00Z","date_published":"2009-05-01T07:00:00Z","updated_at":"2026-07-24T06:07:03Z","subjects":["differential equations","qualitative theory","semigroups","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/59","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Lan Nguyen (Director), Dr. John Spraker,Dr. Di Wu"]},{"key":"dc:creator","label":"Author","values":["Dong, Qian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics and Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["differential equations","qualitative theory","semigroups","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/59"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The qualitative behavior of solutions of differential equations mainly addresses the various questions arising in the study of the long run behavior of solutions. The contents of this thesis are related to three of the major problems of the qualitative theory, namely the stability, the boundedness and the periodicity of the solution. Learning the qualitative behavior of such solutions is crucial part of the theory of differential equations. It is important to know if a solution is bounded or unbounded or if a solution is stable. Moreover, the periodicity of a solution is also of great significance for practical purposes."]},{"key":"dc:title","label":"Title","values":["Qualitative Behavior of Solutions to Differential Equations in <i>R</i><sup><em>n</em></sup> and in Hilbert Space"]}]}],"canonical_facts":{"dc:contributor":["Dr. Lan Nguyen (Director), Dr. John Spraker,Dr. Di Wu"],"dc:creator":["Dong, Qian"],"dc:description.abstract":["The qualitative behavior of solutions of differential equations mainly addresses the various questions arising in the study of the long run behavior of solutions. The contents of this thesis are related to three of the major problems of the qualitative theory, namely the stability, the boundedness and the periodicity of the solution. Learning the qualitative behavior of such solutions is crucial part of the theory of differential equations. It is important to know if a solution is bounded or unbounded or if a solution is stable. Moreover, the periodicity of a solution is also of great significance for practical purposes."],"dc:identifier":["https://digitalcommons.wku.edu/theses/59"],"dc:subject":["differential equations","qualitative theory","semigroups","Mathematics"],"dc:title":["Qualitative Behavior of Solutions to Differential Equations in <i>R</i><sup><em>n</em></sup> and in Hilbert Space"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics and Computer Science"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:07:03Z"}