Ekeland variational principle

Résumé : The Ekeland variational principle formulated by Ivar Ekeland in 1972 is the foundation of modern variational calculus. Its novelty consists in introducing a perturbed variational principle where the goal function f is replaced by the perturbed function f + e¦(·) - xe¦. Its numerous and varied applications are developed and described in this monograph : geometry of Banach spaces nonlinear analysis differential equations and partial differential equations global analysis probabilistic analysis differential geometry fixed point theorems nonlinear semi-groups dynamical systems optimization mathematical programming optimal control. Some of these applications are currently used for modelling in engineering macro-economics and statistics. This monograph is addressed particularly to graduate course lecturers researchers engineers and graduate students.