Compact embeddings for weighted fractional Sobolev spaces and applications to nonlinear Schrödinger equations

The aim of this work is to prove a compact embedding for weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions to the following Schrödinger equation (Formula presented.) where the two measurable functions K>0 and (Formula presented.) could vanish at infinity.