EXISTENCE OF RENORMALIZED SOLUTIONS FOR SOME DEGENERATE AND NON-COERCIVE ELLIPTIC EQUATIONS

This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by - div(b(|u|)|.del u|(p-2)del u) + d(|u|)|del u|(p) = f - div(c(x)|u|(alpha) in Omega, u = 0 where Omega is a bounded open set of R-N (N > 2) with 1 < p < N and f.epsilon L-1(Omega), under some growth conditions on the function b(center dot) and d(center dot), where c(center dot) is assumed to be in LN/(p-1)(Omega). We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.