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

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