We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature. The obtained results can be viewed as a nontrivial extension to the nonlocal setting of some recent contributions already present in the literature.
Appolloni, L., Molica Bisci, G., Secchi, S. (2021). On critical Kirchhoff problems driven by the fractional Laplacian. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(6) [10.1007/s00526-021-02065-8].
On critical Kirchhoff problems driven by the fractional Laplacian
Appolloni L.;Secchi S.
2021
Abstract
We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature. The obtained results can be viewed as a nontrivial extension to the nonlocal setting of some recent contributions already present in the literature.
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