Localization of Nash-type equilibria for systems with partial variational structure

Authors

  • Andrei Stan Faculty of Mathematics and Computer Science, Babeș-Bolyai University & Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat522-1356
Abstract views: 62

Abstract

In this paper, we aim to generalize an existing result by obtaining localized solutions within bounded convex sets, while also relaxing specific initial assumptions. To achieve this, we employ an iterative scheme that combines a fixed-point argument based on the Minty-Browder Theorem with a modified version of the Ekeland variational principle for bounded sets. An application to a system of second-order differential equations with Dirichlet boundary conditions is presented.

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References

A. Stan, Nonlinear systems with a partial Nash type equilibrium, Stud. Univ. Babes-Bolyai Math., 66 (2021) no. 2, pp. 397-408, http://doi.org/10.24193/subbmath.2021.2.14. DOI: https://doi.org/10.24193/subbmath.2021.2.14

I. Benedetti, T. Cardinali, R. Precup, Fixed point-critical point hybrid theorems and application to systems with partial variational structure, J. Fixed Point Theory Appl., 23 (2021) art. no. 63, https://doi.org/10.1007/s11784-021-00852-6. DOI: https://doi.org/10.1007/s11784-021-00852-6

R. Precup, A critical point theorem in bounded convex sets and localization of Nash-type equilibria of nonvariational systems, J. Math. Anal. Appl., 463 (2018), pp. 412-431, https://doi.org/10.1016/j.jmaa.2018.03.035 DOI: https://doi.org/10.1016/j.jmaa.2018.03.035

R. Precup, Nash-type equilibria and periodic solutions to nonvariational systems, Adv. Nonlinear Anal., 3 (2014) no. 4, pp. 197-207, https://doi.org/10.1515/anona-2014-0006. DOI: https://doi.org/10.1515/anona-2014-0006

M. Beldinski, M. Galewski, Nash type equilibria for systems of non-potential equations, Appl. Math. Comput., 385 (2020), pp. 125456, https://doi.org/10.1016/j.amc.2020.125456. DOI: https://doi.org/10.1016/j.amc.2020.125456

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

J. Nash, Non-cooperative games, Ann. Math., 54 (1951) no. 2, pp. 286-295, https://doi.org/10.2307/1969529. DOI: https://doi.org/10.2307/1969529

A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, 1997.

R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Modelling, 49 (2009) no. 3, pp. 703-708, https://doi.org/10.1016/j.mcm.2008.04.006. DOI: https://doi.org/10.1016/j.mcm.2008.04.006

G. Ciarlet, Linear and Nonlinear Functional Analysis with Applications, SIAM, Philadelphia, 2013. DOI: https://doi.org/10.1137/1.9781611972597

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011. DOI: https://doi.org/10.1007/978-0-387-70914-7

R. Precup, Linear and Semilinear Partial Differential Equations, De Gruyter, Berlin, 2013. DOI: https://doi.org/10.1515/9783110269055

A. Cabada, Green’s Functions in the Theory of Ordinary Differential Equations, Springer, New York, 2014. DOI: https://doi.org/10.1007/978-1-4614-9506-2

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Published

2023-12-28

How to Cite

Stan, A. (2023). Localization of Nash-type equilibria for systems with partial variational structure. J. Numer. Anal. Approx. Theory, 52(2), 253–272. https://doi.org/10.33993/jnaat522-1356

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