Bifurcation of positive solutions from zero or infinity in elliptic problems which are not linearizable

The existence of global continua of solutions bifurcating from u = 0 on `bifurcation intervals' surrounding the eigenvalues of the linear problem obtained by putting the nonlinear term equal to zero is proven. These continua have similar properties obtained in Rabinowitz' global bifurcation theorem. The elliptic partial differential problem was also considered in [3], where it was shown that, when M₁ = 0, continua of positive or negative solutions bifurcate from an interval containing the principal eigenvalue. The Sturm-Liouville analogue of (1.1) was studied and extended the previous results to deal with bifurcation from either u = 0 or u = 8, for the general case M₁<0.