The asymptotic behaviour of solutions with blow-up at the boundary for semilinear elliptic problems

By constructing the comparison functions and the perturbed method. it is showed that any solution u is an element of C-2(Omega) to the sernifinear elliptic problems Delta u = k(x)g(u), x is an element of Omega, u vertical bar(a Omega) = +infinity satisfies lim(d(x)-> 0) u(x)/Z(d(mu)(x)) = [(2+sigma)(2+rho+sigma)/2(C0)(2+rho)](1/)rho, where Omega is a bounded domain with smooth boundary in R-N; lim(d(x)-> 0) k(x)/d(sigma)(x) = c(0) -2 < sigma, c(0) > 0, mu = 2+sigma/2; g is an element of C(1)vertical bar 0.similar to), g > 0 and g(s)/s is increasing on (0, infinity), there exists p > 0 such that lim(s) (-similar to) g'(v xi)/g'(v) = xi(rho), for all xi > 0, integral(Z(s))(similar to) dt/root 2G(t) = s. G(t) = integral(0)(t) g(s)ds. (c) 2005 Elsevier Inc. All rights reserved.