Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at $u=0$

Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat

In this paper we consider a semilinear elliptic equation with a strong singularity at $u=0$, namely $ \displaystyle u\geq 0 \mbox{ in } Ω$, $ \displaystyle - div \,A(x) D u = F(x,u…