Existence of explosive positive solutions of quasilinear elliptic equations

In this paper, our main purpose is to consider the quasilinear equation div(vertical bar del u vertical bar(p-2)del u) = m(x)f(u) on a domain Omega subset of R-N, N >= 3, where f is a nonnegative, nondecreasing continuous function which vanishes at the origin. and in is a nonnegative continuous function with the property that any zero of in is contained in a bounded domain in Omega such that m is positive on its boundary. For Omega bounded. we show that a nonnegative solution a satisfying u(x) - infinity as x -> theta Omega exists. For Omega un-boundary (including Omega = R-N) we show that a similar result holds where u(x) -> as vertical bar x vertical bar -> infinity within Omega and u(x) -> infinity as x -> theta Omega. (c) 2005 Elsevier Inc. All rights reserved.