Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another.
","abstract_html":"<p>Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another. </p>","abstract_has_math":false,"creators":["Seelbach, Charley Lockhart"],"institution":"Eastern Kentucky University","degree_name":"Master of Science (MS)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:19Z","subjects":["fixed point theorems","Leggett-Williams fixed-point theorem","Dirichlet boundary conditions","Mathematics"],"languages":[],"rights":["Copyright 2013 Charley Lockhart Seelbach"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Seelbach, Charley Lockhart"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["fixed point theorems","Leggett-Williams fixed-point theorem","Dirichlet boundary conditions","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Charley Lockhart Seelbach"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another.
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"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/133"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2013 Charley Lockhart Seelbach"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["fixed point theorems","Leggett-Williams fixed-point theorem","Dirichlet boundary conditions","Mathematics"],"dc:title":["Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MS)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:19Z"}