The nonlinear second order multi-point boundary value problem , with the boundary conditions is investigated. Here the function is Lipschitz continuous with respect to and is continuous in , and , . The authors suggest a numerical approximating method based upon the shooting method for finding regular solutions and simple fold bifurcation solutions and their structure depending on a parameter.
The other types of boundary conditions and can be investigated analogously. The results of many numerical experiments are given, which show the genericity of the fold bifurcation phenomenon in these problems.