Nonlinear systems with a partial Nash type equilibrium
DOI:
https://doi.org/10.24193/subbmath.2021.2.14Keywords:
Nash-type equilibrium, Perov contraction, Ekeland variational principle, periodic solution.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.
Mathematics Subject Classification (2010): 47H10, 47J30, 34C25.
References
Beldzinski, M., Galewski, M., Nash-type equilibria for systems of non-potential equations, Appl. Math. Comput., 385(2020), 125456.
Benedetti, I., Cardinali, T., Precup, R., Fixed point-critical point hybrid theorems and applications to systems with partial variational structure, submitted.
Cournot, A., The mathematical principles of the theory of wealth, Economic J.,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.
Precup, R., Methods in Nonlinear Integral Equations, Springer, Amsterdam, 2002.
Precup, R., Nash-type equilibria and periodic solutions to nonvariational systems, Adv. Nonlinear Anal., 4(2014), 197-207.
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