Neumann problem with a discontinuous nonlinearity

Choudhuri, Debajyoti (author), Repovš, Dušan (author), Saoudi, Kamel (author)

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is “smooth”.

• Language: English
• Keywords: Neumann problem, discontinuous nonlinearity, nonsmooth Palais-Smale condition
• 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
• Publication date: 01.01.2026
• Year: 2026
• Number of pages: 12 str.
• Numbering: Vol. 59, iss. 1, article no. 20250229
• PID: 20.500.12556/RUL-182175
• UDC: 517.9
• ISSN on article: 2391-4661
• COBISS.SI-ID: 276617987
• Publication date in RUL: 28.04.2026

Record is a part of a journal

• Title: Demonstratio Mathematica
• Shortened title: Demonstr. Math.
• Publisher: De Gruyter Poland
• ISSN: 2391-4661
• COBISS.SI-ID: 526342681

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.

Secondary language

• Language: Slovenian
• Keywords: Neumannov problem, Palais-Smaleov pogoj