A class of elliptic inclusion in fractional Orlicz–Sobolev spaces

Abstract

ABSTRACT We consider an elliptic inclusion that is driven by ( − Δ ) a ( ⋅ ) s called fractional a ( ⋅ ) -Laplacian operator, with Dirichlet-type boundary conditions. We take two different assumptions on the Carathéodory function f . One of them is where f satisfies the localy Lipchitz condition and the other one is when f does not satisfy an assumption of growth. With a regular Clarke subdifferential ∂ C and Lebourg's mean value theorem, by applying a variational approach together with the critical point theory, we obtain a weak solution to the inclusion problem in appropriate fractional Orlicz–Sobolev spaces.