Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems

By applying the properties of the unique classical solution to the singular boundary value problem on half line -p"(s) = y(p(s)),p(s) > 0, s is an element of (0, infinity), p(0) = 0, lim(s-->infinity) p'(s) = b greater than or equal to 0, and constructing the new comparison functions, they show the existence and the optimal global estimates of solutions to singular nonlinear Dirichlet problems -Deltau = k(x)y(u), u > 0, x is an element of Omega, u\(phiOmega) = 0, where Omega is a bounded domain with smooth boundary in R-N; g(s) is nonincreasing and positive in (0, infinity), integral(1)(infinity) g(t) dt < infinity and lim(s-->0+) g(s) = +infinity; k is an element of C-alpha(Omega) is positive in Omega, and may be singular or zero on the boundary. (C) 2004 Elsevier Ltd. All rights reserved.