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We prove a continuous embedding that allows us to obtain a boundary traceimbedding result for anisotropic Musielak-Orlicz spaces, which we then apply toobtain an existence result for Neumann problems with nonlinearities on theboundary associated to some anisotropic nonlinear elliptic equations inMusielak-Orlicz spaces constructed from Musielak-Orlicz functions on which andon their conjugates we do not assume the $\Delta_2$-condition. The uniquenessis also studied.

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