Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (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.

Keywords

nonhomogeneous differential operator;sublinear perturbation;superlinear perturbation;nonlinear regularity;nonlinear maximum principle;comparison principle;minimal positive solution;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956
COBISS: 18481753 Link will open in a new window
ISSN: 1534-0392
Views: 656
Downloads: 336
Average score: 0 (0 votes)
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Other data

Pages: str. 1403-1431
Volume: ǂVol. ǂ18
Issue: ǂno. ǂ3
Chronology: May 2019
DOI: 10.3934/cpaa.2019068
ID: 11191853