1.报告题目：某些离散自治非线性薛定谔方程的基态解

  摘要:In this talk, we will consider the existence of ground state solutions for a class of discrete nonlinear Schr?dinger equations with a sign-changing potential V that converges at infinity and a nonlinear term being asymptotically linear at infinity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is that, due to the convergency of V at infinity, the classical methods such as periodic translation technique and compact inclusion method cannot be employed directly to deal with the lack of compactness of the Cerami sequence. New techniques are developed in this work to overcome these two major difficulties. This enables us to establish the existence of a ground state solution and derive a necessary and sufficient condition for a special case. To the best of our knowledge, this is the first attempt in the literature on the existence of a ground state solution for the strongly indefinite problem under no periodicity condition on the bounded potential and the nonlinear term being asymptotically linear at infinity. This is a joint work with Genghong Lin and Jianshe Yu.

  时间：2021年4月17日 周六上午 9:00-10：20

  报告地点：北主楼1205微格教室

  报告人简介：周展，广州大学二级教授，博士生导师，教育部创新团队带头人，享受国务院政府特殊津贴专家，广州市“优秀专家，先后主持创新团队发展计划2项、国家自然科学基金6项，发表学术论文80余篇。

  2.报告题目：时间离散的时滞反应扩散方程的波前解

  摘要:With the growth of a single species with age structure on an unbounded domain as a prototype, we derive a delayed temporally discrete reaction-diffusion equation. The main result is on the existence of traveling wavefront solutions of the equation. We first transform the problem into that on the existence of fixed points of a mapping. Then by successfully constructing a pair of upper and lower solutions, we establish the existence of traveling wavefront by applying the upper-lower solution method.

  时间：2021年4月17日 周六上午 10:30-11：50

  报告地点：北主楼1205微格教室

  报告人简介：郭志明，广州大学教授，博士生导师，南粤优秀教师，广州市优秀教师，先后主持国家自然科学基金面上项目3项，参加国家自然科学基金重点项目1项，发表学术论文70余篇。

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五邑大学学科与科技（社科）发展中心

数学与计算科学学院

2021年4月14日