Scholarlink

In 1972, French Mathematician I. Ekeland (1944–) published a concise introduction to his variational principle in the “C. R. Acad. Sci. Paris Sér. A-B”, and subsequently provided detailed proofs and many applications in 1974 and 1979 in the JMAA and Bull. AMS, respectively. After 1980s, this principle is commonly referred to as Ekeland’s variational principle. Ekeland’s variational principle discusses the essential characterization of a lower semicontinuous functional f in a complete metric space, suggesting that while it may not have a global minimum, but its suitable perturbed functional does have a global minimizer, and its distance to approximate extreme point of the original functional can be controlled. The proof of this principle is fundamentally based on the completeness of the metric space.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Ekeland Variational Principle and Its Applications

  • 章节

  • 发表日期：

    2026年

查看全文
  • Shiqing Zhang

摘要

In 1972, French Mathematician I. Ekeland (1944–) published a concise introduction to his variational principle in the “C. R. Acad. Sci. Paris Sér. A-B”, and subsequently provided detailed proofs and many applications in 1974 and 1979 in the JMAA and Bull. AMS, respectively. After 1980s, this principle is commonly referred to as Ekeland’s variational principle. Ekeland’s variational principle discusses the essential characterization of a lower semicontinuous functional f in a complete metric space, suggesting that while it may not have a global minimum, but its suitable perturbed functional does have a global minimizer, and its distance to approximate extreme point of the original functional can be controlled. The proof of this principle is fundamentally based on the completeness of the metric space.