Abstract
We study isolated singularities of the quasilinear equation \((*) - div (|\nabla u|^{p - 2} \nabla u) + |u|^{q - 1} u = 0\) in an open set of ℝN, where 1 < p ≦ N, p -1 ≦ q < N(p — 1)/ (N -p). We prove that, for any positive solution, if a singularity at the origin is not removable then either \(|x|^{p/(q + 1 + p)} u(x) \to const. = \gamma _{N,p,q} \) or u(x)/μ(x) → γ γ any positive constant as x → 0 where μ is the fundamental solution of the p-harmonic equation: \( - div(|\nabla \mu |^{p - 2} \nabla \mu ) = \delta _0 \). Global positive solutions are also classified.
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Friedman, A., Véron, L. Singular solutions of some quasilinear elliptic equations. Arch. Rational Mech. Anal. 96, 359–387 (1986). https://doi.org/10.1007/BF00251804
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DOI: https://doi.org/10.1007/BF00251804