A BIFURCATION - TYPE THEOREM FOR SINGULAR NONLINEAR ELLIPTIC EQUATIONS

We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian and exhibiting the combined effects of singular and superlinear terms. Using variational methods combined with truncation and comparison techniques, we prove a bifurcation - type theorem. More precisely, we show that there exists a critical parameter value lambda* > 0 s.t. for all lambda (0, lambda*) (lambda being the parameter) the problem has at least two positive smooth solutions, for lambda = lambda* the problem has at least one positive smooth solution and for lambda > lambda* the positive solutions disappear.