Isolated singularities of solutions to quasi-linear elliptic equations with absorption

We study the problem of removability of isolated singularities for a general second-order quasi-linear equation in divergence form −divA(x,u,∇u)+a0(x,u)+g(x,u)=0 in a punctured domain Ω∖{0}, where Ω is a domain in Rn, n⩾3. The model example is the equation −Δpu+gu|u|p−2+u|u|q−1=0, q>p−1>0, p