科研之友
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摘要
Let N >= 2 and 1 < p < (N + 2)/(N - 2)(+). Consider the Lane-Emden equation Delta u + u(p) = 0 in R-N and recall the classical Liouville type theorem: if u is a non-negative classical solution of the Lane-Emden equation, then u equivalent to 0. The method of moving planes combined with the Kelvin transform provides an elegant proof of this theorem. A classical approach of Serrin and Zou, originally used for the Lane-Emden system, yields another proof but only in lower dimensions. Motivated by this, we further refine this approach to find an alternative proof of the Liouville type theorem in all dimensions.
- 出版日期2017-11
