A geometrical approach to bifurcation for nonlinear boundary value problems
作者： L. Br�ll , H. -P. H�lters
DOI: 10.1007/BF00953673
关键词: Mathematics 、 Bifurcation theory 、 Nonlinear boundary value problem 、 Magnitude (mathematics) 、 Differential equation 、 Mathematical analysis 、 Boundary value problem 、 Second order equation 、 Bifurcation 、 Computation
摘要: In this note we use a new averaging method, which was introduced in [2], to explain the geometrical behaviour of systems governed by nonlinear boundary value problems formy″+g(y)=K sin(Ωt),y(0)=y(π/Ω)=0. We show numerical computations that global features solutions (such as number solutions, their magnitude, bifurcation behaviour, etc.) agree both original and averaged model. As an example, pendulum equation is discussed detail.
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