AN ANALYTICAL-NUMERICAL METHOD FOR A TYPICAL BIFURCATION PROBLEM

In this paper, the nonlinear two-point boundary vslue problem which has a secondary bifurcation point is solved by an anlyticnumerical mechod.The problem was first transformed analytically into finding roots of the trascendental equation Then the turning point was obtained numerically, λ_c=1.87452030182. And the following three cases are all considered: the problem has two solutions, one solution or no solution, when λ<λ_c, λ=λ_c, or λ>λ_c, respectively.The steps for solving the problem and some results of numerical experiments are given in the paper.