Nonlinear systems with a partial Nash type equilibrium


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.


Andrei Stan
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


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

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A. Stan, Nonlinear systems with a partial Nash type equilibrium, Stud. Univ. Babes-Bolyai, Math., 66 (2021) no. 2, 397–408,


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Studia Univ. Babes-Bolyai Math.

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Univ. Babes-Bolyai

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

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

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

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

[5] Nash, J.,Non-cooperative games,Ann. of Math.54(1951), 286-295.

[6] Precup, R.,Methods in Nonlinear Integral Equations, Springer, Amsterdam,2002.

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

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