Existence Results for the Robin p-Laplacian with Concave-Convex Problems and Indefinite Potential

We consider nonlinear Robin problems driven by the p-Laplacian plus and 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 λ > 0. In addition, we show the existence of a smallest positive solution uλ and determine the monotonicity and continuity properties of the map .