The second order expansion of boundary blow-up solutions for infinity-Laplacian equations

In this paper, by using Karamata regular variation theory and a perturbed argument, we study the second order expansion of viscosity solutions to boundary blow-up elliptic problem Delta(infinity) u = b(x) f (u), x is an element of Omega, u vertical bar(partial derivative Omega) = +infinity, where Omega is a bounded domain with C-2-boundary in R-N, b is an element of C((Omega) over bar) is non-negative and non-trivial in Omega, f is an element of C-1([0, infinity)) is a normalized regularly varying function at infinity with index gamma > 3. (C) 2015 Elsevier Inc. All rights reserved.