Isolated singularities of positive solutions of p-Laplacian type equations in R^d

Abstract

We study the behavior of positive solutions of p-Laplacian type elliptic equations of the formand Ω is a domain in R d 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.