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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 Schrödinger equations whose simplest prototype isThe proof is based on the variant Fountain theorem established by Zou.

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In this paper we are concerned with qualitative properties of entire solutions to a Schrödinger equation with sublinear nonlinearity and sign-changing potentials. Our analysis considers three distinct cases and we establish sufficient conditions for the existence of infinitely many solutions.

We consider the following nonlinear Schrödinger equationUsing variational methods, we prove the existence of two solutions with negative and positive energies, one of these solutions being nonnegative.