Existence and multiplicity of positive solutions for parametric nonlinear nonhomogeneous singular Robin problems

We consider nonlinear Robin problems driven by a nonhomogeneous differential operator and with a reaction that has a singular term and a parametric (p - 1)-superlinear perturbation which need not satisfy the Ambrosetti-Rabinowitz condition. We are looking for positive solutions. Using variational arguments and a suitable truncation and comparison techniques, we prove a bifurcation-type theorem which describes the set of positive solutions as the parameter lambda > 0 varies. Also we show the for every admissible value of the parameter lambda > 0, the problem has a smallest solution (u) over bar (lambda) and we determine the monotonicity and continuity properties of the map lambda -> (u) over bar (lambda).