Entropy solutions for some elliptic anisotropic problems involving variable exponent with Fourier boundary conditions and measure data

This paper is devoted to the study of some nonlinear elliptic anisotropic Fourier boundary-value problems, whose prototype is given by {-Au+g(x,u, del u) + delta|u|(p0(x)-2)u = mu - div phi(u) in Omega, Bu + lambda u = h on Omega, where the right hand side mu belongs to (L)1(omega)+W--1,W-(p) over right arrow '(x)((Omega) over bar), the operator Au is a Leray-Lions anisotropic operator and phi is an element of C-0(R,R-N), the nonlinear term g : Omega x R x R-N -> R satisfying some growth condition but no sign condition. We provide an existence result of entropy solutions for this class of anisotropic problems.