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 indefinitepotential. In the reaction we have the competing effects of two nonlinear terms. Oneis parametric and strictly ( p − 1)-sublinear. The other is ( p − 1)-linear. We prove abifurcation-type theorem describing the dependence of the set of positive solutions onthe parameter λ>0. We also show that for every admissible parameter the problem hasa smallest positive solution ¯uλand we study monotonicity and continuity propertiesof the map λ →¯uλ.