EXACT BOUNDARY BEHAVIOR OF SOLUTIONS TO SINGULAR NONLINEAR DIRICHLET PROBLEMS

In this article we analyze the exact boundary behavior of solutions to the singular nonlinear Dirichlet problem -Delta u = b(x)g(u) + lambda a(x) f (u), u > 0, x is an element of Omega, u vertical bar(partial derivative Omega)= 0, where Omega is a bounded domain with smooth boundary in R-N, lambda > 0, g is an element of C-1((0, infinity), (0, infinity)), g(s) = infinity, b, a is an element of C-loc(alpha)(Omega), are positive, but may vanish or be singular on the boundary, and f is an element of C([0, infinity), [0, infinity)).