Positive solutions for generalized nonlinear logistic equations of superdiffusive type

We consider a generalized version of the p-logistic equation. Using variational methods based on the critical point theory and truncation techniques, we prove a bifurcation-type theorem for the equation. So, we show that there is a critical value lambda*> 0 of the parameter lambda> 0 such that the following holds: if lambda> lambda*, then the problem has two positive solutions; if lambda= lambda*, then there is a positive solution; and finally, if 0 < lambda< lambda*, then there are no positive solutions.