Concave-Convex Problems for the Robin p-Laplacian Plus an Indefinite Potential

We consider nonlinear Robin problems driven by the p-Laplacian plus an indefinite potential. In the reaction, we have the competing effects of a parametric concave (that is,(p-1)-sublinear) term and of a convex (that is,(p-1)-superlinear) term which need not satisfy the Ambrosetti-Rabinowitz condition. We prove a "bifurcation-type" theorem describing in a precise way the dependence the dependence of the set of positive solutions on the parameter lambda>0. In addition, we show the existence of a smallest positive solutionu lambda* and determine the monotonicity and continuity properties of the map lambda bar right arrow u(lambda)*.