Abstract: By using the Rabinowitz global bifurcation theorem, the author studies the global structure of nodal solution set of second-order Dirichlet boundary problem, where r is a positive parameter, a: ［0,1］→［0,∞) is continuous and allowed to be constant at 0 in some proper subinterval of ［0,1］. f: R→R is continuous, asymptotically linear at 0 and ∞. There are two non-zero zero points of f.

Key words: bifurcation method, connected branch, zero point, nodal solution