Positive solutions for the Robin p-Laplacian problem with competing nonlinearities

Abstract

We consider a parametric nonlinear elliptic equation driven by the Robin p-Laplacian. The reaction term is a Carathéodory function which exhibits competing nonlinearities (concave and convex terms). We prove two bifurcation-type results describing the set of positive solutions as the parameter varies. In the process we also prove two strong comparison principles for Robin equations. These results are proved for differential operators which are more general than the p-Laplacian and need not be homogeneous.