Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum

In this Note we consider a class of noncoercive nonlinear problems whose prototype is -Delta(p)u + b(x)delu(lambda) = mu in Omega, u = 0 on partial derivativeOmega where Q is a bounded open subset of R-N (N greater than or equal to 2), Delta(p) is the so called p-Laplace operator (1 < p < N) or a variant of it, g is a Radon measure with bounded variation on 2 or a function in L-1 (Omega), lambda greater than or equal to 0 and b belongs to the Lorentz space L-N,L-1 (Omega) or to the Lebesgue space L-infinity(Omega). We prove existence and uniqueness of renormalized solutions. To cite this article: M.F. Betta et al., C R. Acad. Sci. Paris, Ser. I 334 (2002) 757-762. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS