U.S.-China Cooperative Research: Variational and TopologicalMethods in Nonlinear Analysis and Applications to Nonlinear Differential Equations

9723489王本奖项支持美国犹他州立大学王志强与中国科学院数学研究所李树杰的合作研究。主要研究了变分法、临界点理论、莫尔斯理论等新方法的发展，以及这些新方法在非线性微分方程中的应用。该项目将把非线性分析的两个小组聚集在一起，共同解决一个需要两个小组共同解决的问题。中国合作者在相关领域发表了40多篇研究论文，并负责提出局部链接的概念，这是临界点理论处理多重结果的有力工具。美国PI在变分技术和莫尔斯理论方面拥有专业知识。这两个小组的互补性专业知识应能使人们对这一领域产生新的见解。中方将由中国国家自然科学基金提供支持。

9723489 Wang This award supports the initiation of collaborative research between Zhi-Qiang Wang, Utah State University, and Li Shujie, Institute of Mathematics, Chinese Academy of Sciences. The research concerns the development of new methods in calculus of variations, critical point theory, and Morse theory, and the application of these techniques to nonlinear differential equations. The project will bring together two groups in nonlinear analysis to work on a problem that requires the strengths of both groups to address. The Chinese co-PI has over forty research papers in relevant areas, and is responsible for the initiation of the concept of local linking, which is a powerful tool in critical point theory to deal with multiplicity results. The US PI has expertise in variational techniques and in the theory of Morse. The complementary expertise of the two groups should enable new insights into this field. Support on the Chinese side will be provided by the Chinese National Natural Science Foundation.