TY - JOUR AU - Papageorgiou, Nikolaos S. AU - Rădulescu, Vicenţiu D. PY - 2017/10/22 Y2 - 2024/03/28 TI - Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 121 IS - 2 SE - Articles DO - 10.7146/math.scand.a-96696 UR - https://www.mscand.dk/article/view/96696 SP - 263-292 AB - <p>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 $+\infty $ 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 $u^*_{\lambda }$ and investigate the monotonicity and continuity properties of the map $\lambda \mapsto u^*_{\lambda }$.</p> ER -