Bifurcation Analysis of Some Classes of Nonlinear Boundary Value Problems with Parameter
Author(s):
Daria Vladislavovna Chemkaeva
postgraduate in the department of Computional Science and IT,
01.01.07 "Computational mathematics"
Herzen State Pedagogical University.
dariachemkaeva@yahoo.com
Abstract:
This study deals with the number of positive solutions
of an autonomous ordinary differential equation of the
second order with parameter and with homogeneous boundary conditions.
The nonlinear function in the equation is a polynomial of odd degree.
We investigate the number of positive solutions of the problem.
depending on parameter. To find the number of such solutions
we use the Korman-Li-Oyang theorem, which determines the bifurcation
points of boundary value problem. Examples and bifurcation diagrams
confirm the research.
Keywords
- bifurcation diagrams
- exact number of solutions
- Korman–Li–Oyang Theorem
- nonlinear boundary value problem
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