Let Ω be an open bounded domain of ℝN (N≥3) with a smooth boundary. This paper is mainly concerned with the existence and uniqueness of an entropy solution to the following nonlinear anisotropic elliptic problem:
−∑i=1N∂∂xiai(x,∂∂xiu)+|u|pM(x)−2u=finΩ
with boundary condition
∑i=1Nai(x,∂∂xiu)νi=−|u|r(x)−2uon∂Ω,
where f∈L1(Ω) and νi(x) are the outer unit normals to the boundary at x∈∂Ω.

anisotropic equations; variable exponent; weak solutions; entropy solutions; Robin type boundary condition