讲座题目：Double phase problems with competing potentials: concentration and multiplication of ground  states

主办单位：三峡数学研究中心/理学院

报告专家：张健 （湖南工商大学）

报告时间：2023 年 3 月 15 日（周三）下午（15:00-18:00）

报告地点：腾讯会议（ID: 469-554-908）

专家简介：张健，博士，副教授，硕士生导师，主要从事非线性偏微分方程、临界点理论与非线性变分问题的研究。主持国家自然科学基金面上项目1项，国家自然科学基金青年项目1项，博士后科学基金和省部级科研项目5项；在《Math. Z.》、《J. Differential Equations》、《J. Geom. Anal.》、《J. Math. Phys》、《Discrete Contin. Dyn. Sys. A》、《Proc. Amer. Math. Soc.》、《Z. Angew. Math. Phys.》、《Topol. Meth.Nonl. Anal.》、《Comm. Pure Appl. Anal.》等国际刊物上发表SCI学术论文多篇。先后获得湖南省优秀博士学位论文奖，湖南工商大学优秀科研成果一等奖，学术新人奖等。目前担任SCI期刊《Mathematical Methods in the Applied Sciences》、《Rendiconti del Circolo Matematico di Palermo Series 2》和《Analele Stiintifice ale Universitatii Ovidius Constanta》的编委。

报告摘要：In this talk, we will introduce some recent results about the perturbed double phase problem with lack of compactness and competing potentials. More precisely, applying topological and variational tools from Nehari manifold analysis and Ljusternik Schnirelmann category theory, we study the existence of positive ground state solutions and the relation between the number of positive solutions and the topology of the set where the nonlinear potential attains its global minimum and the nonlinear potential attains its global maximum. Moreover, we determine two concrete sets related to the potentials as the concentration positions and we describe the concentration of ground state solutions. Finally, the asymptotic convergence and the exponential decay of positive solutions are also explored.