李翀 副研究员

办公室：思源楼920

邮箱：lichong@amss.ac.cn

研究方向：非线性泛函分析，变分方法及临界点理论，偏微分方程
   

 

代表论文：

1. Chong Li, Shujie Li, Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem, Journal of Functional Analysis, Vo.271, 2016, 245-263.

2. Chong Li, Generalized Poincaré-Hopf theorem and application to nonlinear elliptic problem, Journal of Functional Analysis, Vo.267, 2014, 3783-3814.

3. Chong Li, Shujie Li, Zhaoli, Liu, Bifurcation surfaces stemming from the Fucik spectrum，Journal of Functional Analysis, Vo.263, Issue 12(2012), 4059-4080.

4. Chong Li, Shujie Li, Jiaquan Liu, Splitting theorem, Poincare-Hopf theorem and jumping nonlinear problems, Journal of Functional Analysis, Vo.221, 2005, No.2, 439-455.

5. Chong Li,Shujie Li, Zhaoli Liu, Jianzhong Pan, On the Fucik spectrum, Journal of Differential Equations, Vo.244, 2008, 2498-2528.

6. Chong Li, Shujie Li, Zhaoli Liu, Existence of type(II) region and convexity and concavity of potential functional corresponding jumping nonlinear problems, Calculus of Variations and Partial Differential Equations, Vo.32, 2008, 237-251.

7. Chong Li, The quantitative analysis on the Fucik spectrum and solvability of jumping nonlinear problems, Communications in Contemporary Mathematics, Vo.13, No.2(2011), 293-308.

8. Chong Li, Some remarks on the critical point theory, Topological Methods in Nonlinear Analysis, Vo.30, No.2, 2007.

9. Chong Li, The existence of solutions of elliptic equations with Neumann boundary condition for superlinear problems, Acta Mathematica Sinica, English Series, Dec, 2004, Vo.20, No.6, 965-976.

10. Chong Li, The existence of infinitely many solutions of a class of nonlinear elliptic equations with Neumann boundary condition for both resonance and oscillation problems, Nonlinear Analysis, 54(2003), 431-443.

11. Chong Li, Shujie Li, Multiple solutions and sign changing solutions of a class of nonlinear elliptic equations with Neumann boundary condition, JMAA, 298(2004), No.1, 14-32.

12. 李翀，李树杰，关于临界点理论的几个注记，中国科学，Vo.46, No.5, 1-9, 2016.

13. Chong Li, Yanheng Ding, Shujie Li, Multiple solutions of nonlinear elliptic equations for oscillation problems, JMAA, Vo.303, 2005, 477-485.

14. Chong Li, Shibo Liu, Homology of saddle point reduction and applications to resonant elliptic systems, Nonlinear Analysis, Vo.81(2013), 236-246.

15. Li Ma, Chong Li, Zhao Lin, Monotone solutions to a class of elliptic and diffusion equations, Communication on Pure and Applied Analysis，Vo.6, 2007, No.1, 237-246.

16. Jing Zhang, Chong Li, Xiaoping, Xue, Nontrivial Solutions for a Class of Quasilinear Problems with Jumping Nonlinearities via a  Co-homological Local Splitting, Nonlinear Analysis, Vo.75, Issue 13(2012), 4896–4903.

17. Aixia Qian, Chong Li, Infinitely Many Solutions for a Robin Boundary Value Problem, International Journal of Differential Equations, Vo. 2010, Article ID 548702, 9 pages.

主要工作：

（1）建立C^1光滑的Poincare-Hopf定理；对无穷维形式在下述方面予以改进：（i）将有界Gromoll-Meyer对替换为泛函水平集对；（ii）去掉Morse不等式关于泛函水平集之间只有孤立临界点的限制； (iii)拓广著名的Marino-Prodi扰动定理；

（2）摆脱经典隐函数定理在开集上可微的限制，证明开集稠子集上的隐函数定理，这一进展导致两方面突破，一是利用它建立全新的分支定理（包含经典的Crandall-Rabinbowitz分支定理），二是利用它得到弱光滑条件下局部Morse理论，特别是减弱著名数学家Helmut Hofer相关工作的泛函光滑性条件。

（3）研究高维情况下Fucík谱基本性质，解决人们长期关注的从Fucík谱分出分支曲面的问题。特别是给出Fucík谱(II)型区域存在性的一个充分条件；还证明了Conley同伦指标平凡与临界群平凡之间的等价关系，这一等价关系对跳跃非线性问题可解性起至关重要的作用。

（4）建立一类与Nehari流形有关的新型环绕定理并发现超线性问题的第四个解与椭圆算子谱间隙的紧密联系。