Abstract space ordinary differential equations

Author: Guo DaJun et al.
Publisher:
Publish Date: 2002-10-01
Features: The theory of ordinary differential equations in Banach spaces is a newly developed mathematical branch in the past two to three decades. It combines the theory of ordinary differential equations with functional analysis and utilizes functional analysis methods to study ordinary differential equations in Banach spaces. Its theory has broad applications in various fields such as infinite systems of ordinary differential equations, critical point theory, partial differential equations, and fixed-point theorems. In particular, the descending flow lines commonly used in critical point theory are based on the theory of ordinary differential equations in Banach spaces. Due to its importance and novelty, it has been included as one of the key projects supported by the National Natural Science Foundation of China. In China, there are few researchers studying the theory of ordinary differential equations in Banach spaces. In 1985, at the fifth National Conference on Nonlinear Functional Analysis, the author and Associate Professor Sun Jingxian co-authored a comprehensive report titled The Theory of Ordinary Differential Equations in Banach Spaces, which sparked great interest among many people. This book can clearly serve as a graduate textbook for relevant majors in comprehensive universities and higher normal universities, as well as a reference for teachers and scientific and technological workers engaged in research. The book introduces the theory of ordinary differential equations in Banach spaces, covering topics such as preliminary knowledge, compactness conditions, dissipative conditions, flow-invariant sets, and differential inequalities.