A supercritical nonlocal Neumann problem involving non-homogeneous fractional Laplacian

In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional $g$-Laplace operator with exterior Neumann condition. Our argument exploits some properties of fractional Orlicz-Sobolev spaces combined with a variational principle for nonsmooth functionals, which allows to deal with problems lacking compactness.