中南海外名家讲坛暨微分方程变分方法研讨会系列讲座报告

发布时间:2018年07月09日 作者:唐颖   消息来源:业务办    阅读次数:[]

中南海外名家讲坛暨微分方程变分方法研讨会系列讲座报告 Lecture1: A fibering map approach to semilinear elliptic equations. In this first lecture, we study the combined e_ect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with sign-changing weight functions. With the help of the decomposition of Nehari manifold, we prove that there are at least two positive solutions for the indefinite equation in bounded domains. 主讲人:吴宗芳教授 时间:2018年7月12日8:00-11:40 地点:数学楼145报告厅 Talk1: Existence and concentration of positive solutions for indefinite elliptic equations with steep well potential. In this talk, we will study the existence, multiplicity and concentration of positive solutions for the following indefinite semilinear elliptic equations. We assume that the potential V is a steep well potential and f; g are sign-changing which satisfy suitable conditions. 报告人:吴宗芳教授 时间:2018年7月12日14:00-15:40 地点:数学楼145报告厅 Talk2: The effect of nonlocal term on the k-asymptotically linear Kirchhoff type equations In this talk, we are concerned with a class of k-asymptotically linear Kirchhoff type equations in R^n. Unlike most other studys on this problem, we are more interested in the effect of nonlocal term on the number of nontrivial solutions. By using minimax method as well as Caffarelli-Kohn-Nirenberg inequality, we obtain the non-existence, existence and multiplicity of nontrivial solutions 报告人:孙俊涛副教授 时间:2018年7月12日16:00-17:30 地点:数学楼145报告厅 Lecture2: The effect of domain shape on the number of nontivial solutions for semilinear elliptic equations. In this lecture, we study the decomposition of the filtration of the Nehari manifold via the variation of domain shape. Furthermore, we use this result to prove that the semilinear elliptic equation in some unbounded and bounded domains has multiple positive solutions and we can find at least one ground state solution. 主讲人:吴宗芳教授 时间:2018年7月13日8:00-11:40 地点:数学楼145报告厅 Talk3: On the non-autonomous Schrodinger-Poisson systems in R^3. In this talk, we will study the following non-autonomous Schrodinger-Poisson systems in R^3; By using the fibering maps and studying some properties of the Nehari manifold, we will obtain the existence of positive solutions for the above Schrodinger-Poisson systems. 报告人:吴宗芳教授 时间:2018年7月13日14:00-15:40 地点:数学楼145报告厅 Lecture3: On the linear eigenvalue problems with indefinite weight functions. In this lecture, we exploit the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t -->J(tu); where J is the Euler functional associated with a eigenvalue value problem we discuss how the Nehari manifold changes as l changes and show how existence, non-existence and multiplicity results for positive solutions of the equation are linked to properties of the manifold. 主讲人:吴宗芳教授 时间:2018年7月15日14:00-17:40 地点:数学楼145报告厅 报告人简介: 吴宗芳,高雄大学特聘教授,博士生导师,教务长,教学发展中心主任,台湾数学学会理事,台湾科技部数学推动中心审议委员。主要从事非线性偏微分方程的理论研究,在J. Functional Analysis, J. Differential Equations等国际重要学术期刊发表SCI学术论文70余篇。 孙俊涛,山东理工大学副教授,硕士生导师。2011年6月获得中南大学理学博士学位,2014年12月至2015年12月在美国德克萨斯大学从事博士后研究。先后应邀访问台湾理论科学研究中心、成功大学、高雄大学、美国内华达大学拉斯维加斯分校等机构和高校并作学术报告。主要从事微分方程与动力系统的研究,在J. Differential Equations等国际重要数学期刊上发表SCI论文30余篇,其中6篇入选“ESI高被引论文”。近年来先后主持国家自然科学基金2项(面上项目与青年基金各1项),山东省优青1项,中国博士后科学基金特别资助1项。



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