Nonradial large solutions of sublinear elliptic problems

Let p   be a nonnegative locally bounded function on RNRN, N⩾3N⩾3, and 0<γ<10<γ<1. Assuming that the oscillation sup|x|=rp(x)−inf|x|=rp(x)sup|x|=rp(x)−inf|x|=rp(x) tends to zero as r→∞r→∞ at a specified rate, it is shown that the equation Δu=p(x)uγΔu=p(x)uγ admits a positive solution in RNRN satisfying lim|x|→∞u(x)=∞lim|x|→∞u(x)=∞ if and only if∫RNp(x)|x|N−2dx=∞.