Semilinear fractional elliptic equations with measures in unbounded domain

Furthermore, we analyze properties of weak solution uk to (E) with Ω=RN, ν=kδ0 and h(s)=sp, where k>0, p∈(0,NN−2α) and δ0 denotes Dirac mass at the origin. Finally, we show for p∈(0,1+2αN] that uk→∞ in RN as k→∞, and for p∈(1+2αN,NN−2α) that limk→∞uk(x)=c∣x∣−2αp−1 with c>0, which is a classical solution of (−Δ)αu+up=0 in RN∖{0}.