Boundary Behavior of Solutions to Singular Boundary Value Problems for Nonlinear Elliptic Equations

Let Omega be a bounded domain with smooth boundary in R-N and h is an element of C((0, infinity), (0, infinity)) with lim(s -> 0+) h(s) = Gamma is an element of (0, infinity). By the perturbation method, which is due to Garcia Me hail, and nonlinear transformations and comparison principles, we derive the exact boundary behavior of solutions to a singular Dirichlet problem -Delta v + h(v)/v vertical bar del v vertical bar(2) = b(x), v > 0, x is an element of Omega, v vertical bar partial derivative Omega = 0. 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 Omega and may be (rapidly) vanishing or blow up on the boundary.