Lions-type theorem of the fractional Laplacian and applications

Abstract

In this paper, our goal is to establish a generalized version of Lions-type theorem for the fractional Laplacian. As an application of this theorem, we consider the existence of ground state solutions of a fractional equation:\[(-\Delta)^s u + V (\lvert x \rvert) u = f(u), \; x \in \mathbb{R}^N ,\]where $N \geqslant 3, s \in (\frac{1}{2}, 1), V$ is a singular potential with $\alpha \in (0, 2s) \cup (2s, 2N - 2s)$, and the nonlinearity $f$ has the critical growth, discussed without any boundary value condition.

Topics & Concepts