演講者： 黃信元教授 (國立交通大學應用數學系)

標題：Bubbling Solutions for the Liouville systems in a torus

時間：10月07日早上11點00分

地點：校本部第二綜合大樓8樓 B808 教室

摘要： We consider the following Liouville system on a parallelogram Ω in R 2 :where hi(x) ∈ C 3 (Ω), hi(x) > 0, ui is doubly periodic on ∂Ω(i ∈ I), and A = (aij )n×n is a non-negative constant matrix. We prove that if ∑ q is a non-degenerate critical point of n i=1 ρ ∗ i log hi(x) and A satisfies certain conditions, (1) has a sequence of fully bubbling solutions which blow up at p, as ρ = (ρ1, · · · , ρn) → ρ ∗ = (ρ ∗ 1 , · · · , ρ∗ n ), where ρ ∗ satisfies 8π ∑n i=1 ρ ∗ i = ∑n i=1 ∑n j=1 aijρ ∗ i ρ ∗ j and ∑n i=1 aijρ ∗ i ρ ∗ j > 6π for j ∈ I.