Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential - Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D. (MATHEMATICA SCANDINAVICA, 2017)
We consider a parametric Robin problem driven by the Laplace operator plus an indefinite and unbounded potential. The reaction term is a Carathéodory function which exhibits superlinear growth near +∞ without satisfying the Ambrosetti-Rabinowitz condition. We are looking for positive solutions and prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. We also establish the existence of the minimal positive solution u^*_λ and investigate the monotonicity and continuity properties of the map λ u^*_λ .