On the existence of oscillating solutions in non-monotone Mean-Field Games

For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an oscillatory behaviour when they are close to the trivial (constant) one. The existence of such branches is derived using local and global bifurcation methods, that rely on the analysis of eigenfunction expansions of solutions to the associated linearized problem. Numerical analysis is performed on two different models to observe the oscillatory behaviour of solutions predicted by bifurcation theory, and to study further properties of branches far away from bifurcation points.

• Publication year

  2017

• Venue

  Journal of Differential Equations

• Publication date

  2017-11-21

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1016/J.JDE.2018.12.025arXiv 1711.08047
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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