时间：2021年11月18日（星期四）  下午15:00-17:00

地点：腾讯会议ID:335 345 555

报告题目1：Global multiplicity of solutions for a modified elliptic problem with singular terms

报告人：杨敏波 教授   浙江师范大学

摘要：In this talk, we consider the problem

where  is a smooth bounded domain, are bounded continuous functions,  and is a real parameter. We first prove a comparison principle to prove the existence of a minimal solution by the method of sub and super solutions and then we also obtain the second solution by critical point theory.

报告人简介：杨敏波，浙江师范大学教授，博士生导师，初阳学院副院长，浙江省高校中青年学科带头人浙江省数学会理事、浙江省青科协理事、美国数学评论评论员。主要从事非线性分析及其应用领域的研究，主持或参与多项国家与省级科研项目。在CVPDE、JDE、Com. Anal. Geometry、Nonlinearity、DCDS-A 等杂志发表论文六十余篇。

报告题目2：Global alternative without eigenvalues and its application on normalized solutions for the Schrödinger equation

报告人：钟学秀 副研究员   华南师范大学

摘要：In present paper, we establish a global alternative theorem without eigenvalues, no matter the essential spectrum is a bifurcation point or not. As an application, we also use this theorem to give a new approach to study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form

Compared with the traditional constrained variational method, the advantage of this approach is that we can handle the nonlinearities in a unified way, which are either mass subcritical, mass critical or mass supercritical. It is also crucial to study the asymptotic behaviors of the positive solutions along the global branch as  and .

合作者: Louis Jeanjean (Université de Bourgogne Franche-Comté) and 张建军（重庆交通大学）

报告人简介: 钟学秀，华南师范大学副研究员，华南数学应用与交叉研究中心青年拔尖引进人才。主要研究领域为椭圆偏微分方程、泛函分析和变分法。2015年博士毕业于清华大学，获清华大学优秀博士学位论文一等奖和优秀博士毕业生。2015-2017年在台湾大学理论科学研究中心跟随林长寿教授做博士后。主持国家基金一项，广东省基金两项，广州市基金一项。已在JDG、Math. Ann.、Ann. Sc. Norm. Super. Pisa Cl. Sci.、CVPDE、JDE等国际重要刊物上发表多篇学术论文。

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