Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case

We consider a nonlinear elliptic equation of logistic type, driven by the p-Laplacian differential operator with a general superdiffusive reaction. We show that the equation exhibits a bifurcation phenomenon. Namely there is a critical value lambda(*) of the parameter lambda > 0, such that, if lambda > lambda(*), the equation has two nontrivial positive smooth solutions, if lambda = lambda(*), then there is one positive solution and finally if lambda is an element of (0, lambda(*)) then there is no positive solution