Structure of positive radial solutions including singular solutions to Matukuma's equation
The authors study radial solutions of the semilinear equation \[ \Delta u + \frac{1}{1+ | x | ^2}(u^+)^p=0 \text{ on } \mathbb{R}^3 \setminus \{ (0,0,0) \} \] with \(0<p<5\), using a careful study of the corresponding scalar equation. They obtain information about the asymptotic behaviour of the solution when \(x\) is near \((0,0,0)\) and when \(| x | \rightarrow \infty\). Also they derive information about the changes of sign.
scientific article; zbMATH DE number 5000548