中文摘要：

The multiplicity and bifurcation of a two-point boundary value problem(BVP) of nonlinear differential equations(NLDE) are studied firstly using a manifold method.And by some convenient numerical approaches,the discussion on the solutions to the BVP of two order NLDE is turned into the problem on the intersections of the end manifold with the target manifold defined by the boundary conditions,also the bifurcation diagrams and the numerical solutions to the NLDE are obtained.As an example,a mathematical model describing the deformations of elastic circular bar used as gripper and spring element is discussed.