Infinitely many solutions for a class of fractional Orlicz-Sobolev Schrödinger equations

Abstract

In the present paper, we deal with a new compact embedding theorem for a subspace of the new fractional Orlicz-Sobolev spaces. We also establish some useful inequalities which yields to apply the variational methods. Using these abstract results, we study the existence of infinitely many nontrivial solutions for a class of fractional Orlicz-Sobolev Schrödinger equations whose simplest prototype is $$(-△{)}_m^s+V(x)m(u)u=f(x,u),x\in {\mathbb{R}}^N,$$ where $s\in ]0,1[$, $N\ge 2$, $(-△{)}_m^s$ is fractional $M$-Laplace operator and the nonlinearity $f$ is sublinear as $|u|\to \infty$. The proof is based on the variant Fountain theorem established by Zou.

arXiv admin note: text overlap with arXiv:1901.00784