報(bào) 告 人：李本鳥 博士

報(bào)告題目：Infinitely many dichotomous solutions for elliptic problems

報(bào)告時(shí)間：2023年10月13日（周五）下午14：30-15：30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508學(xué)術(shù)會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

      李本鳥，江西師范大學(xué)講師，博士畢業(yè)于澳大利亞新英格蘭大學(xué)，之后在澳大利亞新英格蘭大學(xué)做博士后研究。主要研究二階橢圓方程解的存在性和唯一性問(wèn)題，在Ann. Sc.Norm. Super. Pisa Cl. Sci.，Calc. Var. PDE, J. Differential Equations，Comm. Contem. Math, Sci. China Math.等國(guó)際知名學(xué)術(shù)期刊上發(fā)表多篇學(xué)術(shù)論文。

報(bào)告摘要：

      In this talk, I will introduce some results about the Schr\odinger-Newton equation. Here, we demonstrate an interesting phenomenon, which we call dichotomy, for concentrating solutions of the above Schr\odinger-Newton equation. More specifically, we show the existence of infinitely many concentrating solutions which concentrate both in a bounded domain and near infinity. In addition, the non-degeneracy of the ground state is established for the above Schr\odinger-Newton equation with non-constant potentials.