Anisotropic singular Neumann equations with unbalanced growth

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

We consider a nonlinear parametric Neumann problem driven by the anisotropic ▫$(p, q)$▫-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter ▫$\lambda$▫ varies. We also show the existence of minimal positive solutions ▫$u_{\lambda }^{\ast}$▫ and determine the monotonicity and continuity properties of the map ▫$\lambda \mapsto u_{\lambda }^{\ast}$▫.

• Language: English
• Keywords: modular function, truncation, comparison principle, minimal solution, anisotropic regularity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Submitted for review: 27.10.2020
• Article acceptance date: 24.01.2021
• Publication date: 01.03.2021
• Year: 2022
• Number of pages: Str. 55-82
• Numbering: Vol. 57, iss. 1
• PID: 20.500.12556/RUL-136915
• UDC: 517.956
• ISSN on article: 0926-2601
• DOI: 10.1007/s11118-021-09905-4
• COBISS.SI-ID: 57450755
• Publication date in RUL: 25.05.2022

Record is a part of a journal

• Title: Potential analysis
• Shortened title: Potential anal.
• Publisher: Kluwer Academic Publishers
• ISSN: 0926-2601
• COBISS.SI-ID: 512523801

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 01.03.2021