Boundary behavior for the solutions to Dirichlet problems involving the infinity-Laplacian

In this paper, by constructing suitable comparison functions, we mainly analyze the exact boundary behavior for the unique solution near the boundary to the singular Dirichlet problem -Delta(infinity)u = b(x)g(u), u > 0, x is an element of Omega, u vertical bar a Omega = 0, where Omega is a bounded domain with smooth boundary in R-N, g is an element of C-1((0,infinity),(0,infinity), g is decreasing on (0, infinity) with lim(s -> 0+) g(s) = infinity, g is normalized regularly varying at zero with index -gamma (gamma > 1) and b is an element of C((Omega) over bar) which is positive in Omega and may be vanishing on the boundary and rapidly varying near the boundary. (C) 2015 Published by Elsevier Inc.