Abstract
Let Ω be a bounded domain with smooth boundary in ℝN and h ∈ C((0,∞), (0,∞)) with lims→0+ h(s) = Υ ∈ (0,∞). By the perturbation method, which is due to García Melián, and nonlinear transformations and comparison principles, we derive the exact boundary behavior of solutions to a singular Dirichlet problem 
. Then, applying the result, combining two kinds of nonlinear transformations, we derive the exact boundary behavior of solutions to a boundary blow-up elliptic problem and a singular Dirichlet problem, where the weight b is positive in Ω and may be (rapidly) vanishing or blow up on the boundary.
Keywords: Differential operator; Hilbert space
Published Online: 2016-03-10
Published in Print: 2010-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
