On the positive solutions of the Matukuma equation. (English) Zbl 0801.35024
The author proves that for \(1< p<5\) every positive entire solution \(u\) (also with infinite total mass) of the Matukuma equation
\[
\Delta u+{1\over 1+| x|^ 2} u^ p= 0\quad\text{in }\mathbb{R}^ 3
\]
is radially symmetric about the origin and \(u_ r< 0\) in \(r>0\). This completes the results obtained before by Y. Li and W.-M. Ni [Arch. Ration. Mech. Anal. 108, No. 2, 175-194 (1989; Zbl 0705.35039); ibid. 118, No. 3, 223-243 (1992; Zbl 0764.35014)].
Reviewer: V.Mustonen (Oulu)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
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