Perturbations of nonlinear eigenvalue problems
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

Abstract
We 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.

Language: English nonhomogeneous differential operator, sublinear perturbation, superlinear perturbation, nonlinear regularity, nonlinear maximum principle, comparison principle, minimal positive solution 1.01 - Original Scientific Article PEF - Faculty of Education 2019 Str. 1403-1431 Vol. 18, no. 3 517.956 1534-0392 10.3934/cpaa.2019068 18481753 438 285 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Communications on pure and applied analysis Commun. pure appl. anal. AIMS Press 1534-0392 15066457