Bifurcation and multiplicity results for critical magnetic fractional problems

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.

Keywords

• Fractional magnetic operators
• critical nonlinearities
• variational methods