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Multiple Positive Solutions for Kirchhoff-Type Problems Involving Supercritical and Critical Terms

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Abstract

We investigate the multiplicity results of positive solutions for a Kirchhoff-type problems with supercritical and critical nonlinear terms in a ball. By employing the Nehari method and Lusternik–Schnirelmann category theory to an auxiliary problems, we note that there is a relationship between the number of maxima in the coefficient function of the critical term and the number of positive solutions for the problems.

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Acknowledgements

The authors express their gratitude to the reviewer for careful reading and helpful suggestions which led to an improvement of the original manuscript. This work was supported by the National Natural Science Foundation of China (No. 11661021) and the Natural Science Research Project of Department of Education of Guizhou Province (Grant Nos. QJJ2023012, QJJ2023061, QJJ2023062).

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Authors and Affiliations

  1. Department of Information Engineering, Guiyang Institute of Information Science and Technology, Guiyang, 550025, China

    Deke Wu

  2. School of Date Sciences and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

    Hongmin Suo

  3. School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China

    Jun Lei

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  1. Deke Wu
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  2. Hongmin Suo
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  3. Jun Lei
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All authors contributed equally to the different parts of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Deke Wu.

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Wu, D., Suo, H. & Lei, J. Multiple Positive Solutions for Kirchhoff-Type Problems Involving Supercritical and Critical Terms. Qual. Theory Dyn. Syst. 23, 139 (2024). https://doi.org/10.1007/s12346-024-00999-w

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