Existence of solutions for a class of porous medium type equations with lower order terms

This paper deals with a class of degenerate quasilinear elliptic equations of the form -div(a(x, u, del u)) + F(x, u, del u) = f, where a(x, u, del u) is allowed to degenerate with the unknown u. Under some hypothesis on a, F, and f, we obtain the existence of bounded solutions u is an element of W-0(1,p) (Omega) boolean AND L-infinity(Omega). For the case f is an element of L-1(Omega), we also prove that there exists at least one renormalized solution.