Singular solutions of some quasilinear elliptic equations (Q1089506)

The authors study the equation \[ -div( | Du|^{p-2} Du)+| u|^{q-1} u=0 \] in an open set of \(R^ N\), \(1<p\leq N\), p-1\(\leq q<N(p-1)/(N-p)\). The result proved is the following. Consider a positive solution with a nonremovable singularity at the origin then either: \((1)\quad | x|^{p/(q+1-p)} u(x)\to c_{N,p,q}\) as \(x\to 0\); \((2)\quad u(x)/m(x)\to c\) (c positive constant depending on u) as \(x\to 0\) where \(-div( | Dm|^{p-2} Dm)=\delta_ 0\) in distribution sense i.e., m is the fundamental solution of the p-harmonic equation. Global solutions are also classified.