Monotonicity results in half spaces for quasilinear elliptic equations involving a singular term

We consider positive solutions to ${\displaystyle -{\mathrm{\Delta }}_{p}u=\frac{1}{u^{\gamma }}+f(u)}$ under zero Dirichlet condition in the half space. Exploiting a prio-ri estimates and the moving plane technique, we prove that any solution is monotone increasing in the direction orthogonal to the boundary.