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Monotone and pseudomonotone operators with applications to variational problems
Includes bibliographical references
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613307487125504 |
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| access_status_str | Open Access |
| author | Alexander, Byron Joseph |
| author2 | Ebobisse Bille, Francois |
| author_browse | Alexander, Byron Joseph Ebobisse Bille, Francois |
| author_facet | Ebobisse Bille, Francois Alexander, Byron Joseph |
| author_sort | Alexander, Byron Joseph |
| collection | Thesis |
| description | Includes bibliographical references |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15464 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:03.682Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15464 Monotone and pseudomonotone operators with applications to variational problems Alexander, Byron Joseph Ebobisse Bille, Francois Mathematics and Applied Mathematics Includes bibliographical references This work is primarily concerned with investigating how monotone and pseudomonotone operators between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a Sobolev space to its dual. We seek to study the abstract theory which underpins this approach and proves the existence of a solution to the equation A (u) = f, implying the existence of a weak solution to the elliptic boundary value problem. Further, we examine properties of monotone and pseudomonotone operators, with an emphasis on a characterization, which involves the latter, and establishes a connection between the operator and the principal part of a partial differential equation. In addition, results relating monotone and pseudomonotone operators with variational inequalities are explored. 2015-11-30T13:11:56Z 2015-11-30T13:11:56Z 2015 Master Thesis Masters MSc http://hdl.handle.net/11427/15464 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Alexander, Byron Joseph Monotone and pseudomonotone operators with applications to variational problems |
| thesis_degree_str | Master's |
| title | Monotone and pseudomonotone operators with applications to variational problems |
| title_full | Monotone and pseudomonotone operators with applications to variational problems |
| title_fullStr | Monotone and pseudomonotone operators with applications to variational problems |
| title_full_unstemmed | Monotone and pseudomonotone operators with applications to variational problems |
| title_short | Monotone and pseudomonotone operators with applications to variational problems |
| title_sort | monotone and pseudomonotone operators with applications to variational problems |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/15464 |
| work_keys_str_mv | AT alexanderbyronjoseph monotoneandpseudomonotoneoperatorswithapplicationstovariationalproblems |