Uniqueness results for nonlinear elliptic equations with a lower order term

We prove the uniqueness of the weak solution of noncoercive nonlinear elliptic problems whose model isu∈W01,p(Ω),-div(a(x)(1+|∇u|2)(p-2)/2∇u)+b(x)(1+|∇u|2)(σ+1)/2=finD′(Ω),where Ω is a bounded open subset of RN, N⩾2, p satisfies p⩾2N/(N+1), a is a function belonging to L∞(Ω) such that a(x)⩾α>0, f belongs to the dual space W-1,p′(Ω), b belongs to some Lebesgue space Lr(Ω) with r⩾r*(N,p) and σ belongs to the interval [0,σ*(N,p,r)], with σ*(N,p,r) and r*(N,p) functions which are specified below.