Abstract
We consider the bifurcation curve of (sign-changing and nonnegative) solutions of the boundary blow-up problem where λ is a positive bifurcation parameter and f is locally Lipschitz continuous at all points in R except possibly at some point s where f(s)=0 and f is continuous there. In particular, when we give a simple explicit formula of the bifurcation curves on the （λ，ρ）-plane, where ρ=min_{x\in (0,1)}u(x). We also study asymptotic behavior of the bifurcation curve for f being asymptotically of the form left or right as u rightarrow infty or infty or 0^{+} or 0^{-}.