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

Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro

• 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 u∗ λ and determine the monotonicity and continuity properties of the map λ → u∗λ.