A critical point theorem in bounded convex sets and localization of Nash-type equilibria of nonvariational systems

Abstract

The localization of a critical point of minimum type of a smooth functional is obtained in a bounded convex conical set defined by a norm and a concave upper semicontinuous functional. A vector version is also given in order to localize componentwise solutions of variational systems. The technique is then used for the localization and multiplicity of Nash-type positive equilibria of nonvariational systems. Applications are given to periodic problems.

Authors

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Critical point; Nash-type equilibrium; Ekeland’s principle; Periodic problem, Positive solution; Multiple solutions

Paper coordinates

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), 412-431, https://doi.org/10.1016/j.jmaa.2018.03.035

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About this paper

Journal

Journal of Mathematical Analysis and Applications

Publisher Name

Elsevier

Print ISSN
Online ISSN

0022-247X

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