Ekeland’s variational principle is a fundamental theorem in nonconves analysis. Its general statement is as the following:Ekeland’s Variational Principle"’a:. Let V be a complete metric space, and F: F—*-RU{ ...Ekeland’s variational principle is a fundamental theorem in nonconves analysis. Its general statement is as the following:Ekeland’s Variational Principle"’a:. Let V be a complete metric space, and F: F—*-RU{ + °°} a lower semicontinuous function, not identically +00 and bounded from, below. Let s>0 be given, and a point u^V such thatF(u)<infF+e.vThen there exists some point v ￡ V such that展开更多
文摘Ekeland’s variational principle is a fundamental theorem in nonconves analysis. Its general statement is as the following:Ekeland’s Variational Principle"’a:. Let V be a complete metric space, and F: F—*-RU{ + °°} a lower semicontinuous function, not identically +00 and bounded from, below. Let s>0 be given, and a point u^V such thatF(u)<infF+e.vThen there exists some point v ￡ V such that
