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This study is about a nonlinear anisotropic problem with homogeneous Neumann boundary condition. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solution, and by approximation methods, we achieve a result of existence and uniqueness of entropy solution.

ENTROPY SOLUTIONS FOR NONLINEAR ELLIPTIC ANISOTROPIC PROBLEMS WITH HOMOGENEOUS NEUMANN BOUNDARY CONDITION