{"id":{"repo_id":"uno","oai_identifier":"oai:scholarworks.uno.edu:td-1882"},"canonical_url":"https://search.dev.ndltd.org/etd/uno/oai:scholarworks.uno.edu:td-1882","repository":{"repo_id":"uno","name":"University of New Orleans","base_url":"https://scholarworks.uno.edu/do/oai/"},"display":{"title":"Multiple Solutions on a Ball for a Generalized Lane Emden Equation","abstract":"In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding.","abstract_html":"In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding.","abstract_has_math":false,"creators":["Khanfar, Abeer"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Saxton, Ralph","Wei, Dongming","Santanilla, Jairo"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-12-19T08:00:00Z","date_published":"2008-12-19T08:00:00Z","updated_at":"2026-07-24T05:28:50Z","subjects":["p-laplacian","critical Sobolev exponents","weighted Sobolev spaces"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uno.edu/td/901","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Saxton, Ralph","Wei, Dongming","Santanilla, Jairo"]},{"key":"dc:creator","label":"Author","values":["Khanfar, Abeer"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["p-laplacian","critical Sobolev exponents","weighted Sobolev spaces"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uno.edu/td/901"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding."]},{"key":"dc:title","label":"Title","values":["Multiple Solutions on a Ball for a Generalized Lane Emden Equation"]}]}],"canonical_facts":{"dc:contributor":["Saxton, Ralph","Wei, Dongming","Santanilla, Jairo"],"dc:creator":["Khanfar, Abeer"],"dc:description.abstract":["In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding."],"dc:identifier":["https://scholarworks.uno.edu/td/901"],"dc:subject":["p-laplacian","critical Sobolev exponents","weighted Sobolev spaces"],"dc:title":["Multiple Solutions on a Ball for a Generalized Lane Emden Equation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:28:50Z"}