Ekeland’s variational principle

Let (M,d) be a complete metric space and let ψ:M(-,+], ψ+, be a lower semicontinuous function which is bounded from below. Then the following hold: For every ε>0 and for any z0M there exists zM such that

  • (i)


  • (ii)

    ψ(x)ψ(z)-εd(x,z), for any xM.

Title Ekeland’s variational principle
Canonical name EkelandsVariationalPrinciple
Date of creation 2013-03-22 15:19:16
Last modified on 2013-03-22 15:19:16
Owner ncrom (8997)
Last modified by ncrom (8997)
Numerical id 8
Author ncrom (8997)
Entry type Theorem
Classification msc 49J40