Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear perturbation. For the first case we show that for ▫$\lambda < \widehat{\lambda}_{1}$▫ (▫$\widehat{\lambda}_{1}$▫ being the principal eigenvalue) there is one positive solution which is unique under additional conditions on the perturbation term. For ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. In the superlinear case, for ▫$\lambda < \widehat{\lambda}_{1}$▫ we have at least two positive solutions and for ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. For both cases we establish the existence of a minimal positive solution ▫$\bar{u}_{\lambda}$▫ and we investigate the properties of the map ▫$\lambda \mapsto \bar{u}_{\lambda}$▫. indefinite and unbounded potential Robin eigenvalue problem sublinear perturbation superlinear perturbation maximum principle positive solution minimal positive solution true false true Angleški jezik Angleški jezik Članek v reviji 2019-09-10 14:31:58 2019-09-10 14:31:59 2021-04-20 13:07:22 0000-00-00 00:00:00 2017 0 0 Str. 2589-2618 no. 5 Vol. 37 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 517.956 1078-0947 http://dx.doi.org/10.3934/dcds.2017111 17925721 15865689 RAZ_Papageorgiou_Nikolaos_Socrates_i2017.pdf RAZ_Papageorgiou_Nikolaos_Socrates_i2017.pdf 1 DC1F13B75030F063799CD98CD44771F6 1b381e63b58d0d16c046ac2c6662859ff12a4fa69e5bf71da2769ca867c2c2ed fed72d0e-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121547 Pedagoška fakulteta