Positive solutions for nonlinear Robin problems with indefinite potential and competing nonlinearities

We consider a nonlinear Robin problem associated to the p-Laplacian plus an indefinite potential. In the reaction we have the competing effects of two nonlinear terms. One is parametric and strictly ( p - 1)-sublinear. The other is ( p - 1)-linear. We prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. > 0. We also showthat for every admissible parameter the problem has a smallest positive solution u. and we study monotonicity and continuity properties of the map.. (u) over tilde (lambda).