Existence of renormalized solutions for some degenerate and non-coercive elliptic equations

Abstract

. This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by where Ω is a bounded open set of R N ( N > 2) with 1 < p < N and f ∈ L 1 (Ω) , under some growth conditions on the function b ( · ) and d ( · ) , where c ( · ) is assumed to be in L N/ ( p − 1) (Ω) . We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.