This research direction originated from the applied differential equations direction led by Mr. Xiao Shutie and was one of the main research directions of the applied mathematics doctoral program approved by the State Council in 1984. In recent years, it has developed very rapidly and now includes several research areas such as functional analysis theory and its applications in differential equations, the theory of nonlinear (complex) ordinary differential equations and its applications, microlocal analysis and its applications, and nonlinear partial differential equations and their applications in geometry and physics. Currently, there are 7 professors and 2 associate professors, all holding doctoral degrees and having overseas work experience, among whom 4 hold doctoral degrees from foreign or overseas institutions.