On the critical $p$-Kirchhoff equation
DOI:
https://doi.org/10.12775/TMNA.2021.061Keywords
$p$-Kirchhoff equation, critical Sobolev exponent, existence, multiplicity, Morse theory, Fadell-Rabinowitz cohomological index, cohomological local splittingAbstract
We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for the $(\text{PS})$ condition to hold. Then we prove some existence and multiplicity results using tools from Morse theory, in particular, the notion of a cohomological local splitting and eigenvalues based on the Fadell-Rabinowitz cohomological index.References
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Copyright (c) 2023 Erisa Hasani, Kanishka Perera
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