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Singular solutions of some quasilinear elliptic equations
Authors:Avner Friedman  Laurent Véron
Institution:(1) Purdue University, Lafayette, Indiana;(2) Université de Tours, France
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 Ropf N , where 1 < p lE N, p -1 lE 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)/mgr(x) rarr gamma gamma any positive constant as x rarr 0 where mgr is the fundamental solution of the p-harmonic equation: 
$$ - div(|\nabla \mu |^{p - 2} \nabla \mu )  =  \delta _0 $$
. Global positive solutions are also classified.
Keywords:
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