The Neumann problem for a class of generalized Kirchhoff-type potential systems

Chems Eddine, Nabil (author), Repovš, Dušan (author)

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter. We show that the problem has at least one solution, which converges to zero in the norm of the space as the real positive parameter tends to infinity, via combining the truncation technique, variational method, and the concentration–compactness principle for variable exponent under suitable assumptions on the nonlinearities.

• Language: English
• Keywords: Kirchhoff-type problems, Neumann boundary conditions, p(x)-Laplacian operator, generalized capillary operator, Sobolev spaces with variable exponent, critical Sobolev exponents, concentration–compactness principle, critical point theory, truncation technique
• 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
• Year: 2023
• Number of pages: 33 str.
• Numbering: Vol. 2023, art. 19
• PID: 20.500.12556/RUL-144647
• UDC: 517.956
• ISSN on article: 1687-2770
• DOI: 10.1186/s13661-023-01705-6
• COBISS.SI-ID: 144015107
• Publication date in RUL: 07.03.2023

Record is a part of a journal

• Title: Boundary value problems
• Shortened title: Bound. value probl.
• Publisher: Springer Nature
• ISSN: 1687-2770
• COBISS.SI-ID: 62113025

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.