EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 54 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 54
Number of page(s) 49
DOI https://doi.org/10.1051/cocv/2026037
Published online 07 July 2026
  1. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. II. Horizon fini et contrôle optimal. C. R. Math. Acad. Sci. Paris 343 (2006) 679–684. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Wilde and P. Kokotovic, A dichotomy in linear control theory. IEEE Trans. Automatic Control 17 (1972) 382–383. [Google Scholar]
  3. A. Porretta and E. Zuazua, Long time versus steady state optimal control. SIAM J. Control Optim. 51 (2013) 4242–4273. [Google Scholar]
  4. E. Trélat and C. Zhang, Integral and measure-turnpike properties for infinite-dimensional optimal control systems. Math. Control Signals Syst. 30 (2018) Art. 3, 34. [Google Scholar]
  5. E. Trélat, C. Zhang and E. Zuazua, Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces. SIAM J. Control Optim. 56 (2018) 1222–1252. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Trélat and E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control. J. Diff. Equ. 258 (2015) 81–114. [Google Scholar]
  7. E. Trélat and E. Zuazua, Turnpike in optimal control and beyond: a survey. arXiv:2503.20342 (2025). [Google Scholar]
  8. P. Cardaliaguet, J.-M. Lasry, P.-L. Lions and A. Porretta, Long time average of mean field games. Netw. Heterog. Media 7 (2012) 279–301. [Google Scholar]
  9. P. Cardaliaguet, J.-M. Lasry, P.-L. Lions and A. Porretta, Long time average of mean field games with a nonlocal coupling. SIAM J. Control Optim. 51 (2013) 3558–3591. [Google Scholar]
  10. E. Bayraktar and X. Zhang, Solvability of infinite horizon McKean-Vlasov FBSDEs in mean field control problems and games. Appl. Math. Optim,. 87 (2023) Paper No. 13, 26. [Google Scholar]
  11. P. Cardaliaguet and A. Porretta, Long time behavior of the master equation in mean field game theory. Anal. PDE 12 (2019) 1397–1453. [Google Scholar]
  12. A. Cecchin, G. Conforti, A. Durmus and K. Eichinger, The exponential turnpike phenomenon for mean field game systems: weakly monotone drifts and small interactions. arXiv:2409.09193 (2024). [Google Scholar]
  13. M. Cirant and A. Mészáros, Long time behavior and stabilization for displacement monotone mean field games. arXiv:2412.14903 (2025). [Google Scholar]
  14. M. Cirant and A. Porretta, Long time behavior and turnpike solutions in mildly non-monotone mean field games. ESAIM Control Optim. Calc. Var. 27 (2021) Paper No. 86, 40. [CrossRef] [EDP Sciences] [Google Scholar]
  15. M. Bardi and H. Kouhkouh, Long-time behavior of deterministic mean field games with nonmonotone interactions. SIAM J. Math. Anal. 56 (2024) 5079–5098. [Google Scholar]
  16. R. Carmona, Q. Cormier and H.M. Soner, Synchronization in a Kuramoto mean field game. Commun. Part. Diff. Equ. 48 (2023) 1214–1244. [Google Scholar]
  17. A. Cesaroni and M. Cirant, Stationary equilibria and their stability in a Kuramoto MFG with strong interaction. Commun. Part. Diff. Equ. 49 (2024) 121–147. [Google Scholar]
  18. N. Mimikos-Stamatopoulos and S. Munoz, Regularity and long time behavior of one-dimensional first-order mean field games and the planning problem. SIAM J. Math. Anal. 56 (2024) 43–78. [Google Scholar]
  19. P. Cardaliaguet and M. Masoero, Weak KAM theory for potential MFG. J. Diff. Equ. 268 (2020) 3255–3298. [Google Scholar]
  20. M. Cirant, On the existence of oscillating solutions in non-monotone mean-field games. J. Diff. Equ. 266 (2019) 8067–8093. [Google Scholar]
  21. A. Cesaroni and M. Cirant, Brake orbits and heteroclinic connections for first order mean field games. Trans. Am. Math. Soc. 374 (2021) 5037–5070. [Google Scholar]
  22. J. Berry, O. Ley and F.J. Silva, Approximation and perturbations of stable solutions to a stationary mean field game system. J. Math. Pures Appl. 194 (2025) 103666. [Google Scholar]
  23. A. Briani and P. Cardaliaguet, Stable solutions in potential mean field game systems. Nonlinear Diff. Equ. Appl. 25 (2017) 1. [Google Scholar]
  24. A. Porretta, On the turnpike property for mean field games. Minimax Theory Appl. 3 (2018) 285–312. [Google Scholar]
  25. V.I. Bogachev, N.V. Krylov, M. Röckner and S.V. Shaposhnikov, Fokker-Planck–Kolmogorov equations, vol. 207 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2015). [Google Scholar]
  26. D. Bakry, F. Barthe, P. Cattiaux and A. Guillin, A simple proof of the Poincaré inequality for a large class of probability measures including the log-concave case. Electron. Commun. Probab. 13 (2008) 60–66. [Google Scholar]
  27. A. Cesaroni and M. Cirant, Concentration of ground states in stationary mean-field games systems. Anal. PDE 12 (2019) 737–787. [Google Scholar]
  28. M. Cirant, A. Cosenza and G. Verzini, Ergodic mean field games: existence of local minimizers up to the Sobolev critical case. Calc. Var. Part. Diff. Equ. 63 (2024) Paper No. 134, 23. [Google Scholar]
  29. M. Cirant, F. Kong, J. Wei and X. Zeng, Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost. J. Math. Pures Appl. 198 (2025) Paper No. 103687, 60. [Google Scholar]
  30. F. Kong, Y. Tong and X. Zeng, Local minimizers in second order mean-field games systems with choquard coupling. Electron. J. Probab. 31 (2026) 1–70. [Google Scholar]
  31. F. Kong, Y. Tong, X. Zeng and H. Zhou, Blow-up behaviors of ground states in ergodic mean-field games systems with hartree-type coupling. [Google Scholar]
  32. A.R. Mészáros and F.J. Silva, On the variational formulation of some stationary second-order mean field games systems. SIAM J. Math. Anal. 50 (2018) 1255–1277. [Google Scholar]
  33. B. Pellacci, A. Pistoia, G. Vaira and G. Verzini, Normalized concentrating solutions to nonlinear elliptic problems. J. Diff. Equ. 275 (2021) 882–919. [Google Scholar]
  34. J. Wei, On single interior spike solutions of the Gierer-Meinhardt system: uniqueness and spectrum estimates. Eur. J. Appl. Math. 10 (1999) 353–378. [Google Scholar]
  35. M. Bardi and P. Cardaliaguet, Convergence of some mean field games systems to aggregation and flocking models. Nonlinear Anal. 204 (2021) Paper No. 112199, 24. [Google Scholar]
  36. M. Cirant and E. Continelli, Uniqueness of solutions to MFG systems with large discount. arXiv:2510.09280 (2025). [Google Scholar]
  37. L. Krugel, T. Faulwasser and L. Grüne, Local turnpike properties in finite horizon optimal control, In 2023 62nd IEEE Conference on Decision and Control (CDC) (2023) 5273–5278. [Google Scholar]
  38. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224. Springer (1977). [Google Scholar]
  39. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Uralceva, Linear and quasilinear equations of parabolic type, vol. 23 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI (1968). Translated from the Russian by S. Smith. [Google Scholar]
  40. G.M. Lieberman, Second Order Parabolic Differential Equations. World Scientific Publishing Co., Inc., River Edge, NJ (1996). [Google Scholar]
  41. M. Cirant and D. Ghilli, Existence and non-existence for time-dependent mean field games with strong aggregation. Math. Ann. 383 (2022) 1285–1318. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.