On a class of fully anisotropic elliptic equations

We consider a class of nonlinear elliptic equations driven by a fully anisotropic elliptic operator, and with a Carathéodory reaction. The elliptic operator depends on x and on the gradient of u, via the differential (with respect to u) of a general function belonging to a class of admissible functions. We present also several examples showing how our theorem incorporates the non-radial case, as well as that of functions with no polynomial growth.