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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Bibliographic Details
Main Authors: A. Kirichuka, F. Sadyrbaev
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/302185
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Summary: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.
ISSN:1085-3375
1687-0409