Anisotropic Neumann problems in Sobolev spaces with variable exponent

We prove a trace theorem that allows the treatment of Neumann problems with nonlinearities on the boundary in anisotropic spaces with variable exponent. Then we proceed to the study of such a problem that involves general operators of the p→(⋅)-Laplace type. We deduce the existence of solutions and we direct attention to the situation where the solution is unique.