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

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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
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Number of pages:Str. 1403-1431
Numbering:Vol. 18, no. 3
PID:20.500.12556/RUL-108753 This link opens in a new window
ISSN on article:1534-0392
DOI:10.3934/cpaa.2019068 This link opens in a new window
COBISS.SI-ID:18481753 This link opens in a new window
Publication date in RUL:19.07.2019
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Record is a part of a journal

Title:Communications on pure and applied analysis
Shortened title:Commun. pure appl. anal.
Publisher:AIMS Press
COBISS.SI-ID:15066457 This link opens in a new window

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