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, del u) + a(0)(x, u) + g(x, u) = 0 in a punctured domain Omega\{0}, where Omega is a domain in R-n, n >= 3. The model example is the equation -Delta(p)u + gu vertical bar u vertical bar(p-2) + u vertical bar u vertical bar(q-1) = 0, q > p-1 > 0, p < n. Assuming that the lower-order terms satisfy certain non-linear Kato-type conditions, we prove that for q >= n(p-1)/n-p all point singularities of the above equation are removable, thus extending the seminal result of Brezis and Veron. (c) 2007 Elsevier Inc. All rights reserved.