讲座题目：Bi-harmonic equations involving critical exponential growth on entire space

主办单位：三峡数学研究中心

报告专家：朱茂春博士（江苏大学）

报告时间：2021年9月24日（周五）下午（14:30—16: 30）

报告地点：腾讯会议（ID：493 664 457）

专家简介： 朱茂春，江苏大学副教授。主要研究方向：几何不等式、非线性微分方程。相关研究工作发表在Adv. Math., Analysis & PDE., Calc. Var. & PDE., J. Differntial Equations., Proc. Amer. Math. Soc. 等国际知名学术期刊；主持国家自然科学基金青年项目和面上基金各一项，江苏省青年基金一项。

报告摘要：In this talk, I will report our recent work on the Bi-harmonic equations with critical exponential growth on the entire space. For this kind equations, the possibility of loss of compactness not only produced by the concentration phenomena, but also the vanishing phenomena. The classical method to exclude the vanishing phenomena is using the Schwarz symmetrization or the coercive potential. In our higher order case with non-coercive potential, the lack of Schwarz symmetrization brings us more difficulty. We will show that the Bi-harmonic equations with critical exponential growth on the entire space still have ground states under different assumptions on the potentials by using Fourier rearrangement or a new non-symmetric argument.