## 解析学火曜セミナー

開催情報 火曜日　16:00～17:30　数理科学研究科棟(駒場) 126号室 石毛 和弘, 坂井 秀隆, 伊藤 健一 https://www.ms.u-tokyo.ac.jp/seminar/analysis/

### 2019年11月05日(火)

16:50-18:20   数理科学研究科棟(駒場) 128号室
Ngô Quốc Anh 氏 (ベトナム国家大学ハノイ校 / 東京大学)
Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space (English)
[ 講演概要 ]
This talk concerns entire, non-trivial, non-negative solutions and/or entire, positive solutions to the simplest models of polyharmonic equations with power-type nonlinearity $\Delta^m u = \pm u^\alpha$ in $\mathbb R^n$ with $n \geqslant 1$, $m \geqslant 1$, and $\alpha \in \mathbb R$. For small $m$, the above equations arise in many physical phenomena and applied mathematics. They also arise from several prescribing geometric curvture problems in conformal geometry such as the Yamabe problem, the scalar curvature problem, and the Q-curvature problem for the Paneitz operator. Higher-order cases also arise from the Q-curvature problem for the GJMS operator. In this talk, I will present a complete picture of the existence and non-existence of solutions to the above equations in the full rage of the parameters $n$, $m$, and $\alpha$. This is joint work with V.H. Nguyen, Q.H. Phan, and D. Ye.