报告题目：Non-degeneracy and Some Existence Results for Subcritical Fractional Schr\odinger Equations
时 间：2021年10月8日（星期五）上午9：30
地 点：腾讯ID:576941320
主 办：数学与统计学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和学生
报告摘要：In this talk, we are concerned with the subcritical fractional Schr\odinger equations and study two kinds of problems under different potential conditions. The first problem is about the non-degeneracy of the infinitely many multi-spike solutions concentrated at infinite points at infinity. Moreover, we apply this non-degeneracy property to construct new solutions under some different weighted norm. In the second problem, we consider a class of degenerate potentials with non-isolated critical points, and obtain the existence and local uniqueness of the multi-spike normalized solutions concentrated at k points.
The part of existence results of these two kinds of problems are obtained by use of the Lyapunov-Schmidt reduction method. While in the study of properties of the solutions, different local pohozaev identities are used flexibly. We overcome the difficulties from the nonlocal operator to derive the pointwise decay estimates of the solutions, and construct various local pohozaev identities. In addition, the relatively weak algebraic decay of the ground state solution of the limit fractional equation causes a lot of trouble.
报告人简介：郭青，女，中央民族大学理学院，副教授，研究生导师。2012年博士毕业于中国科学院数学与系统科学研究院，师从曹道民研究员。主要研究非线性色散方程和非线性椭圆方程及方程组。目前已主持两项国家自然科学基金项目，最近五年以第一作者或通讯作者身份在包括Comm. PDE、JDE等微分方程主流期刊发表SCI学术论文十余篇。2020年入选国家民委中青年英才培养计划。