Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis

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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Main Authors: A. Kirichuka, F. Sadyrbaev
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/302185
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spelling doaj-cc7c2871fd5e4c5fbf5da459e308b6e32020-11-25T00:45:20ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author A. Kirichuka
F. Sadyrbaev
spellingShingle A. Kirichuka
F. Sadyrbaev
Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis
Abstract and Applied Analysis
author_facet A. Kirichuka
F. Sadyrbaev
author_sort A. Kirichuka
title 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_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_sort multiple positive solutions for the dirichlet boundary value problems by phase plane analysis
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2015-01-01
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.
url http://dx.doi.org/10.1155/2015/302185
work_keys_str_mv AT akirichuka multiplepositivesolutionsforthedirichletboundaryvalueproblemsbyphaseplaneanalysis
AT fsadyrbaev multiplepositivesolutionsforthedirichletboundaryvalueproblemsbyphaseplaneanalysis
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