On construction of converging sequences to solutions of boundary value problems
We consider the Dirichlet problem x″ = f(t,x), x(a) = A, x(b) = B under the assumption that there exist the upper and lower functions. We distinguish between two types of solutions, the first one, which can be approximated by monotone sequences of solutions (the so called Jackson—Schrader's sol...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2010-04-01
|
| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/5997 |
| _version_ | 1818891038617501696 |
|---|---|
| author | Maria Dobkevich |
| author_facet | Maria Dobkevich |
| author_sort | Maria Dobkevich |
| collection | DOAJ |
| description | We consider the Dirichlet problem x″ = f(t,x), x(a) = A, x(b) = B under the assumption that there exist the upper and lower functions. We distinguish between two types of solutions, the first one, which can be approximated by monotone sequences of solutions (the so called Jackson—Schrader's solutions) and those solutions of the problem, which cannot be approximated by monotone sequences. We discuss the conditions under which this second type solutions of the Dirichlet problem can be approximated.
First published online: 09 Jun 2011 |
| first_indexed | 2024-12-19T17:34:27Z |
| format | Article |
| id | doaj.art-8f75a6fc0c974e6295cda5c023d8e525 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T17:34:27Z |
| publishDate | 2010-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-8f75a6fc0c974e6295cda5c023d8e5252022-12-21T20:12:22ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102010-04-0115210.3846/1392-6292.2010.15.189-197On construction of converging sequences to solutions of boundary value problemsMaria Dobkevich0Daugavpils University Parades str. 1, LV-5400 Daugavpils, LatviaWe consider the Dirichlet problem x″ = f(t,x), x(a) = A, x(b) = B under the assumption that there exist the upper and lower functions. We distinguish between two types of solutions, the first one, which can be approximated by monotone sequences of solutions (the so called Jackson—Schrader's solutions) and those solutions of the problem, which cannot be approximated by monotone sequences. We discuss the conditions under which this second type solutions of the Dirichlet problem can be approximated. First published online: 09 Jun 2011https://journals.vgtu.lt/index.php/MMA/article/view/5997nonlinear boundary value problemstypes of solutionsmonotone iterationsmultiplicity of solutionsnon‐monotone iterations |
| spellingShingle | Maria Dobkevich On construction of converging sequences to solutions of boundary value problems Mathematical Modelling and Analysis nonlinear boundary value problems types of solutions monotone iterations multiplicity of solutions non‐monotone iterations |
| title | On construction of converging sequences to solutions of boundary value problems |
| title_full | On construction of converging sequences to solutions of boundary value problems |
| title_fullStr | On construction of converging sequences to solutions of boundary value problems |
| title_full_unstemmed | On construction of converging sequences to solutions of boundary value problems |
| title_short | On construction of converging sequences to solutions of boundary value problems |
| title_sort | on construction of converging sequences to solutions of boundary value problems |
| topic | nonlinear boundary value problems types of solutions monotone iterations multiplicity of solutions non‐monotone iterations |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/5997 |
| work_keys_str_mv | AT mariadobkevich onconstructionofconvergingsequencestosolutionsofboundaryvalueproblems |