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

Abstract EN

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.