Existence of large solutions for a class of quasilinear elliptic equations

We consider the quasilinear elliptic equation div(vertical bar del u vertical bar(p-2)del u) = a(x) f(u), u >= 0 in Omega, where p > 1, a(x) >= 0, a(x) not equivalent to 0, a(x) is an element of C((Omega) over bar), and f is continuous and non-decreasing on [0, +infinity), satifies f(0) = 0, f(s) > 0 for s > 0 and the Keller-Osserman condition integral(+infinity)(1) [F(s)](-1/p) ds = +infinity, F(s) = integral(s)(0) f(t)dt. We establish conditions on the function a that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation. (C) 2007 Elsevier Inc. All rights reserved.