ABSTRACT
We consider an elliptic inclusion that is driven by called fractional -Laplacian operator, with Dirichlet-type boundary conditions. We take two different assumptions on the Carathéodory function . One of them is where satisfies the localy Lipchitz condition and the other one is when does not satisfy an assumption of growth. With a regular Clarke subdifferential 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.
Acknowledgments
The author would like to thank the anonymous referee for carefully reading the manuscript and for his/her useful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).