Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

Abstract

We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is (p- 1) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter λ> 0 varies. Also we prove the existence of a minimal positive solution uλ∗ and determine the monotonicity and continuity properties of the map λ→uλ∗.