EMBEDDING THEOREMS IN THE FRACTIONAL ORLICZ-SOBOLEV SPACE AND APPLICATIONS TO NON-LOCAL PROBLEMS

In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional Orlicz-Sobolev Schrodinger equations whose simplest prototype is (-Delta)(m)(s) u+ V(x)m(u) = f (x, u), x is an element of R-d, where 0 < s < 1, d >= 2 and (-Delta)(m)(s) is the fractional M-Laplace operator. The proof is based on the variant Fountain theorem established by Zou.