Ekeland variational principle - with generalizations and variants

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.