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Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

In this note we present some uniqueness and comparison results for a class of problem of the form \begin{equation} \label{EE0} \begin{array}{c} - L u = H(x,u,\nabla u)+ h(x), \quad u \in H^1_0(Ω) \cap L^{\infty}(Ω), \end{array} \end{equation} where $Ω\subset \R^N$, $N \geq 2$ is a bounded domain, $L$ is a general elliptic second order linear operator with bounded coefficients and $H$ is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.