Singular solutions for divergence-form elliptic equations involving regular variation theory: Existence and classification

We generalise and sharpen several recent results in the literature regarding the existence and complete classification of the isolated singularities for a broad class of nonlinear elliptic equations of the form(0.1)−div(A(|x|)|∇u|p−2∇u)+b(x)h(u)=0in B1∖{0}, where Br denotes the open ball with radius r>0 centred at 0 in RN (N≥2). We assume that A∈C1(0,1], b∈C(B1‾∖{0}) and h∈C[0,∞) are positive functions associated with regularly varying functions of index ϑ, σ and q at 0, 0 and ∞ respectively, satisfying q>p−1>0 and ϑ−σ