Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and L^(1)-Data

This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusionβ(u)+A(u)+g(x,u,Du)■f,where A is a Leray-Lions operator from W^(1,p)_(0)(Ω)into its dual,βmaximal monotone mapping such that 0∈β(0),while g(x,s,ξ)is a nonlinear term which has a growth condition with respect toξand no growth with respect to s but it satisfies a signcondition on s.The right hand side f is assumed to belong to L^(1)(Ω).