(untitled) (Analysis in Theory and Applications, 2014)
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x,Du)+F(u)) i f in Ω , where fL^1(Ω ). A vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L^1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.