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  • On critical variable-order Kirchhoff type problems with variable singular exponent
    Zuo, Jiabin ; Choudhuri, Debajyoti ; Repovš, Dušan, 1954-
    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.
    Source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 514, iss.1, Oct. 2022, art. 126264 (18 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2022
    Language - english
    COBISS.SI-ID - 106082051

    Link(s):

    https://www.sciencedirect.com/science/article/pii/S0022247X22002785
    Repository of the University of Ljubljana – RUL
    DOI

source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 514, iss.1, Oct. 2022, art. 126264 (18 str.))
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