Perturbations of nonlinear eigenvalue problems

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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
• 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
• Year: 2019
• Number of pages: Str. 1403-1431
• Numbering: Vol. 18, no. 3
• PID: 20.500.12556/RUL-108753
• UDC: 517.956
• ISSN on article: 1534-0392
• DOI: 10.3934/cpaa.2019068
• COBISS.SI-ID: 18481753
• Publication date in RUL: 19.07.2019

Record is a part of a journal

• Title: Communications on pure and applied analysis
• Shortened title: Commun. pure appl. anal.
• Publisher: AIMS Press
• ISSN: 1534-0392
• COBISS.SI-ID: 15066457