168幸运飞艇计划

摘要：In this talk we will talk about the blow-up behaviors of solutions to the singular Liouville type equation with exponential Neumann boundary condition. We generalize the Brezis-Merle type concentration-compactness Theorem to this Neumann problem. Then along the line of the Li-Shafrir type quantization property we show that the blow-up value $m(0) \in 2\pi\N \cup \{ 2\pi(1+\alpha)+2\pi (\N\cup \{0\})\}$ if the singular point $0$ is a blow-up point. In the end, when the boundary value of solutions has an additional condition, we can obtain the precise blow-up value $m(0)=2\pi(1+\alpha)$.