Perturbations of nonlinear eigenvalue problemsPapageorgiou, Nikolaos (Avtor)
Rǎdulescu, Vicenţiu (Avtor)
Repovš, Dušan (Avtor)
nonhomogeneous differential operatorsublinear perturbationsuperlinear perturbationnonlinear regularitynonlinear maximum principlecomparison principleminimal positive solutionWe consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive solutions changes as the real parameter ▫$\lambda$▫ varies. We also show that there exists a minimal positive solution ▫$\overline{u}_\lambda$▫ and determine the monotonicity and continuity properties of the map ▫$\lambda\mapsto\overline{u}_\lambda$▫. Special attention is given to the particular case of the ▫$p$▫-Laplacian.20192019-07-19 11:26:13Neznano108753sl