Bifurcation phenomena for the positive solutions of semilinear elliptic problems with mixed boundary conditions

We consider a parametric semilinear elliptic equation with a Carathéodory reaction which exhibits competing nonlinearities. It is concave (sublinear) near the origin and convex (superlinear) or linear near infty. Usingvariational methods based on the critical point theory, coupled with suitabletruncation and comparison techniques, we prove a bifurcation-type theorem, describing the set of positive solutions as the parameter varies.