报告题目：Discrete boundary value problems with the mean curvature operator

报告人：广州大学周展教授

报告时间：2023年10月27日10:00-11:00

报告地点：立志楼A423

摘要：In this talk, we will introduce some results on the positive solutions for some nonlinear discrete Dirichlet boundary value problems with the mean curvature operator by using critical point theory. First, some sufficient conditions on the existence of infinitely many positive solutions are given. We show that, the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. Then, the existence of at least two positive solutions is established when the nonlinear term is not oscillatory both at the origin and at infinity. Examples are also given to illustrate our main results at last.

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。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》、《J. Dynam. Diff. Eqn.》、《J. Geom. Anal.》、《Nonlinearity》、《Physica D》和《中国科学》(英文版)等重要学术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”第六批先进个人称号。