Nonlinear systems with a partial Nash type equilibrium

Andrei Stan

Abstract


In this paper fixed point arguments and a critical point technique are
combined leading to hybrid existence results for a system of three operator
equations where only two of the equations have a variational structure. The
components of the solution which are associated to the equations having a
variational form represent a Nash-type equilibrium of the corresponding
energy functionals. The result is achieved by an iterative scheme based on
Ekeland's variational principle.


Keywords


Nash-type equilibrium; Perov contraction; Ekeland variational principle; Periodic solution

Full Text:

PDF

References


Be ldzinski, M., Galewski, M.,Nash–type equilibria for systems of non-potentialequations, Appl. Math. Comput.385(2020), 125456.

Benedetti, I., Cardinali, T., Precup, R.,Fixed point-critical point hybrid theo-rems and applications to systems with partial variational structure, submitted.

Cournot, A.,The mathematical principles of the theory of wealth,EconomicJ.,1838.

Mawhin, J., Willem, M.,Critical Point Theory and Hamiltonian Systems,Springer, Berlin, 1989.

Nash, J.,Non-cooperative games,Ann. of Math.54(1951), 286-295.[6] Precup, R.,Methods in Nonlinear Integral Equations, Springer, Amsterdam,2002.

Precup, R.,Nash-type equilibria and periodic solutions to nonvariational sys-tems, Adv. Nonlinear Anal.4(2014), 197-207




DOI: http://dx.doi.org/10.24193/subbmath.2021.2.14

Refbacks

  • There are currently no refbacks.