On critical variable-order Kirchhoff type problems with variable singular exponent

Zuo, Jiabin (author), Choudhuri, Debajyoti (author), Repovš, Dušan (author)

We establish a continuous embedding $W^{s(\cdot),2}(\Omega) \hookrightarrow L^{\alpha (\cdot)}(\Omega)$, where the variable exponent $\alpha(x)$ can be close to the critical exponent $2_s^\ast = \frac{2N}{N-2\bar{s}(x)}$, with $\bar{s}(x) = s(x,x)$ for all $x \in \bar{\Omega}$. Subsequently, this continuous embedding is used to prove the multiplicity of solutions for critical nonlocal degenerate Kirchhoff problems with a variable singular exponent. Moreover, we also obtain the uniform $L^\infty$-estimate of these infinite solutions by a bootstrap argument.

• Language: English
• Keywords: fractional Laplacian of variable-order, continuous embedding, genus, symmetric mountain pass theorem, variable singular exponent
• 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: 2022
• Number of pages: 18 str.
• Numbering: Vol. 514, iss. 1, art. 126264
• PID: 20.500.12556/RUL-136441
• UDC: 517.956
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2022.126264
• COBISS.SI-ID: 106082051
• Publication date in RUL: 04.05.2022

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

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• 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.