Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis
We consider boundary value problems for scalar differential equation x′′+λfx=0, x(0)=0, x(1)=0, where f(x) is a seventh-degree polynomial and λ is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifu...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/302185 |
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| author | A. Kirichuka F. Sadyrbaev |
| author_facet | A. Kirichuka F. Sadyrbaev |
| author_sort | A. Kirichuka |
| collection | DOAJ |
| description | We consider boundary value problems for scalar differential equation x′′+λfx=0, x(0)=0, x(1)=0, where f(x) is a seventh-degree polynomial and λ is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes. |
| format | Article |
| id | doaj-art-cc7c2871fd5e4c5fbf5da459e308b6e3 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cc7c2871fd5e4c5fbf5da459e308b6e32025-08-20T03:19:31ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/302185302185Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane AnalysisA. Kirichuka0F. Sadyrbaev1Daugavpils University, 13 Vienības Street, Daugavpils LV-5401, LatviaInstitute of Mathematics and Computer Science of University of Latvia, Raina Bulvaris 29, Riga LV-1469, LatviaWe consider boundary value problems for scalar differential equation x′′+λfx=0, x(0)=0, x(1)=0, where f(x) is a seventh-degree polynomial and λ is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes.http://dx.doi.org/10.1155/2015/302185 |
| spellingShingle | A. Kirichuka F. Sadyrbaev Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis Abstract and Applied Analysis |
| title | Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis |
| title_full | Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis |
| title_fullStr | Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis |
| title_full_unstemmed | Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis |
| title_short | Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis |
| title_sort | multiple positive solutions for the dirichlet boundary value problems by phase plane analysis |
| url | http://dx.doi.org/10.1155/2015/302185 |
| work_keys_str_mv | AT akirichuka multiplepositivesolutionsforthedirichletboundaryvalueproblemsbyphaseplaneanalysis AT fsadyrbaev multiplepositivesolutionsforthedirichletboundaryvalueproblemsbyphaseplaneanalysis |