Abstract: In this paper, the nonlinear two-point boundary value problem
u"+λ²e^u=0(λ>0),u(0)=0=u(1)
which has a secondary bifurcation point is solved by an anlyticnumerical method.
The problem was first transformed analytically into finding roots of the trascendental equation
2√2/t ln(t+√t²-1)=λ(t > 1).
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.