The shooting method and the analysis of the target map via the degree theory

Events

Presentation Name：	The shooting method and the analysis of the target map via the degree theory
Presenter👷🏿：	Prof. Congming Li
Date：	2012-01-10
Location🥲：	光华东主楼1501
Abstract：	We introduce and analysis the `target map' for the shooting method. For a large class of elliptic systems as well as more general dynamic systems, we show that the target map is onto via the degree theo- ry. The target map is onto implies that we can shoot to any desired position. Applying our result to a motivating example, we obtain the ex- istence of global positive solutions to the Hardy-Littlewood-Sobolev (also known as Lane-Emden) type system. in the critical and supercritical case. On the other hand, the Lane-Emden conjecture state that when k = 1, the above system admits no positive solution in the subcritical case. The Lane-emden conjecture has been proved for many cases and no counter-example has been found yet. This new approach to the shooting method is simple and powerful. We expect many more applications of it.
Annual Speech Directory🈹：	No.4

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