Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side

Abstract. In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is −div(a(x)(1 + jruj2) p−22 ru) + b(x)(1 + jruj2) 2 = f in Ω; u = 0 on @Ω; where Ω is a bounded open subset of RN, N 2, 2−1=N < p < N, a belongs to L1(Ω), a(x) 0> 0, f is a function in L1(Ω), b is a function in Lr(Ω) and 0 < (N; p; r); for some r and (N; p; r). Mathematics Subject Classication. 35J25, 35J60. Received February 11, 2002. Dedicated to the memory of Jacques-Louis Lions, an exceptional mathematician and an exceptional ma