Isolated singularities of positive solutions of p -Laplacian type equations in RdRd

We study the behavior of positive solutions of p-Laplacian type elliptic equations of the formQ′(u):=−Δp(u)+V|u|p−2u=0in Ω∖{ζ} near an isolated singular point ζ∈Ω∪{∞}ζ∈Ω∪{∞}, where 11d>1. We obtain removable singularity theorems for positive solutions near ζ. In particular, using a new three-spheres theorems for certain solutions of the above equation near ζ we prove that if V belongs to a certain Kato class near ζ   and p>dp>d (respectively, p