Robin problems with indefinite linear part and competition phenomenaPapageorgiou, Nikolaos S. (Avtor) Rǎdulescu, Vicenţiu (Avtor) Repovš, Dušan (Avtor) indefinite potentialRobin boundary conditionstrong maximum principletruncationcompeting nonlinearpositive solutionsregularity theoryminimal positive solutionWe consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a superlinear (convex) term. The superlinearity is not expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general hypothesis is used. We prove a bifurcation-type theorem describing the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies. We also show the existence of a minimal positive solution ▫$\tilde{u}_\lambda$▫ and determine the monotonicity and continuity properties of the map ▫$\lambda \mapsto \tilde{u}_\lambda$▫.20172019-09-12 14:17:10Članek v reviji110196UDK: 517.956.2ISSN pri članku: 1534-0392DOI: 10.3934/cpaa.2017063COBISS_ID: 18010713OceCobissID: 15066457sl