Nonradial large solutions of sublinear elliptic problems

Let p be a nonnegative locally bounded function on RN, N 3, and 0 < γ < 1. Assuming that the oscillation sup|x|=r p(x) − inf|x|=r p(x) tends to zero as r →∞at a specified rate, it is shown that the equation Δu = p(x)uγ admits a positive solution in RN satisfying lim|x|→∞ u(x)=∞if and only if RN p(x) |x|N−2 dx=∞. © 2006 Elsevier Inc. All rights reserved