Nonexistence of positive solutions of −Δu=K(x)up in Rn

For p≥0, let σ=n+2−p(n−2). Let K(x) be nonnegative in Rn and satisfy the conditions that |x|σ2K(x) is nondecreasing along each ray {tξ∣t>0} for any unit vector ξ∈Rn and lim|x|→+∞|x|σ2K(x)=+∞. For p<1, assume in addition that K(x) is locally bounded in Rn∖{0}. Then −Δu=K(x)up possesses no positive solutions.