| 报告题目： | On the Fucik spectrum |
| 报 告 人： | 刘兆理 教授 |
| 首都师范大学数学系 | |
| 报告时间： | 2013.6.2(周日）上午10:00-11：00 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | 刘兆理，首都师范大学数学系主任，国家杰出青年基金获得者，教育部长江学者特聘教授。长期从事临界点理论及其应用研究，发展了下降流不变集方法，并将这一新方法成功地应用于非线性椭圆型微分方程理论，在解的存在性、解的个数、变号解的个数、变号解nodal域的个数等方面获得了一批新结果，解决了多个疑难问题。 摘要: In this talk we will discuss several properties concerning the Fucik spectrum. In particular, we will study existence of C^1 curves in the Fucik spectrum, existence of the type (II) region surrounded by the Fucik spectrum, solvability and unique solvability, number of nodal domains of solutions, and bifurcation of solutions from the Fucik spectrum. Since operators stemming from these problems are not in C^1, we have to prove invariant implicit function theorems and invariant bifurcation theorems. This is joint work with Chong Li, Shujie Li, and Jianzhong Pan. |
