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

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 − pu + gu|u|p−2 + u|u|q−1 = 0, q > p − 1 > 0, p