Imbedding results in Musielak-Orlicz spaces with an application to anisotropic nonlinear Neumann problems

We prove a continuous embedding that allows us to obtain a boundary trace imbedding result for anisotropic Musielak-Orlicz spaces, which we then apply to obtain an existence result for Neumann problems with nonlinearities on the boundary associated to some anisotropic nonlinear elliptic equations in Musielak-Orlicz spaces constructed from Musielak-Orlicz functions on which and on their conjugates we do not assume the ${\mathrm{\Delta }}_2$-condition. The uniqueness is also studied.