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

A. Kirichuka and F. Sadyrbaev

Abstract and Applied Analysis, 2015, vol. 2015, issue 1

Abstract: We consider boundary value problems for scalar differential equation x′′ + λf(x) = 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.

Date: 2015
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https://doi.org/10.1155/2015/302185

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:302185

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