报告题目：Ground state solutions for a class of discrete nonlinear Schrödinger equations

报告人：周展教授

报告单位：广州大学

报告时间：2022年5月27日(周五)下午16:00-17:00    

报告地点：腾讯会议, 会议ID：370 190 988

报告摘要：We study the existence of ground state solutions for a class of discrete nonlinear Schrödinger 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 Prof. Jianshe Yu and Dr. Genghong Lin.

报告人简介：周展，博士、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”，中国数学会理事。现任广州大学应用数学研究中心执行主任。 2000年9月前往加拿大访问一年；还应邀访问香港城市大学、加拿大罗瑞尔大学、西安大略大学、新布伦瑞克大学。

先后主持长江学者和创新团队发展计划2项、国家自然科学基金7项、教育部优秀青年教师资助计划、高等学校博士点基金等科研项目多项。近年来在《J. Differential Equations》、《Nonlinearity》、《Physica D》和《中国科学》(英文版)等重要刊物发表高水平科研论文100多篇，先后获得广东省自然科学一等奖(第三)、湖南省科技进步一等奖(第五)、湖南省自然科学优秀论文一等奖、第五届“秦元勋数学奖”、广东省高等学校“千百十人才培养工程”第六批先进个人。

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联系人：李先义