(untitled) (Analysis in Theory and Applications, 2023)
This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusion β(u)+A(u)+g(x,u,Du) i f, where A is a Leray-Lions operator from W^1,p_0(Ω) into its dual, β maximal monotone mapping such that 0 ∈ β(0), while g(x,s, ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s but it satisfies a sign-condition on s. The right hand side f is assumed to belong to L^1(Ω).