Positive solutions for nonlinear nonhomogeneous parametric Robin problems

We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Caratheodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter lambda > 0 approaches zero, we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally, we show that for every admissible parameter value, there is a smallest positive solution u*(A) of the problem, and we investigate the properties of the map lambda -> u*A.