Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data

We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is $$\{\begin{array}{ll}-{\mathrm{\Delta }}_{p}u=H(u)\mu & \text{in }\mathrm{\Omega },\\ u>0& \text{in }\mathrm{\Omega },\\ u=0& \text{on }\mathrm{\partial }\mathrm{\Omega }\mathrm{.}\end{array}$$ Here $\mathrm{\Omega }$ is an open bounded subset of ${\mathbb{R}}^N$ ($N\ge 2$), $\Delta_p u:= \operatorname{div}(|\nabla u|^{p-2}\nabla u)$($1<p<N$)isthe$p$-laplacianoperator,$\mu$ is a nonnegative bounded Radon measure on $\mathrm{\Omega }$ and $H(s)$ is a continuous, positive and finite function outside the origin which grows at most as $s^{-\gamma }$, with $\gamma \ge 0$, near zero.