Parametric nonlinear nonhomogeneous Robin problems

Abstract

We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus a parametric potential term. The reaction is superlinear. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter lambda in R moves. Also we show the existence of a minimal positive solution and prove its monotonicity and continuity properties as a function of the parameter. Finally we show the existence of a nodal solution.