Statement of The Theorem
Let (X, d) be a complete metric space, and let F: X → R ∪ {+∞} be a lower semicontinuous functional on X that is bounded below and not identically equal to +∞. Fix ε > 0 and a point u ∈ X such that
Then there exists a point v ∈ X such that
and, for all w ≠ v,
Read more about this topic: Ekeland's Variational Principle
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