Nash-type equilibria and periodic solutions to nonvariational systems

Abstract

The paper deals with variational properties of fixed points for contraction-type operators. Under suitable conditions, the unique fixed point of a vector-valued operator is a Nash-type equilibrium of the corresponding energy functionals. This is achieved by an iterative scheme based on Ekeland's variational principle. An application to periodic solutions for second order differential systems is given to illustrate the theory.

Keywords

• nash-type equilibrium
• fixed point
• critical point
• ekeland principle
• periodic solution
• second order system
• 47h10
• 47j30
• 34c25