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

Abstract

We consider positive solutions to $-{\Delta }_{p}u=\frac{1}{u^{\gamma }}+f(u)$ 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.

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