The paper deals with variational properties of xed points for contraction-type operators. Undersuitable conditions, the unique xed point of a vector-valued operator is a Nash-type equilibrium of thecorresponding energy functionals. This is achieved by an iterative scheme based on Ekeland’s variationalprinciple. An application to periodic solutions for second order dierential systems is given to illustratethe theory.
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Nash-type equilibrium; fxed point; critical point; Ekeland principle; periodic solution; secondorder system
R. Precup, Nash-type equilibria and periodic solutions to nonvariational systems, Adv. Nonlinear Anal., 3 (2014), no. 4, 197-207, https://doi.org/10.1515/anona-2014-0006
Advances Nonlinear Analysis
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