Isolated singularities of positive solutions of p-Laplacian type equations in [formula omitted

Abstract

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∪{∞}, where 1<p<∞, and Ω is a domain in Rd with d>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>d (respectively, p<d), then any positive solution u of the equation Q′(u)=0 in a punctured neighborhood of ζ=0 (respectively, ζ=∞) is in fact continuous at ζ. Under further assumptions we find the asymptotic behavior of u near ζ.