Electron. J. Differential Equations, Vol. 2018 (2018), No. 153, pp. 1-18.

Bifurcation and multiplicity results for critical magnetic fractional problems

Alessio Fiscella, Eugenio Vecchi

Abstract:
This article concerns the bifurcation phenomena and the existence of multiple solutions for a non-local boundary value problem driven by the magnetic fractional Laplacian $(-\Delta)_{A}^{s}$. In particular, we consider
$$ (-\Delta)_{A}^{s}u =\lambda u + |u|^{2^{\ast}_s -2} u \quad\text{in }\Omega, \quad u=0\quad \text{in }\mathbb{R}^{n}\setminus \Omega, $$
where $\lambda$ is a real parameter and $\Omega \subset \mathbb{R}^n$ is an open and bounded set with Lipschitz boundary.

Submitted April 6, 2018. Published August 13, 2018.
Math Subject Classifications: 35R11, 35Q60, 35A15, 35B33.
Key Words: Fractional magnetic operators; critical nonlinearities; variational methods.

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Alessio Fiscella
Departamento de Matemática
Universidade Estadual de Campinas, IMECC
Rua Sérgio Buarque de Holanda 651
Campinas, SP CEP 13083-859 Brazil
email: fiscella@ime.unicamp.br
Eugenio Vecchi
Dipartimento di Matematica
Sapienza Universitá di Roma
P.le Aldo Moro 5, 00185, Roma, Italy
email: vecchi@mat.uniroma1.it

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