Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 34
Number of page(s) 32
DOI https://doi.org/10.1051/cocv/2023083
Published online 02 April 2025
  1. M. Bardi and F.S. Priuli, Linear-quadratic N-person and mean-field games with ergodic cost. SIAM J. Control Optim. 52 (2014) 3022–3052. [Google Scholar]
  2. G. Barles, J. Meireles, On unbounded solutions of ergodic problems in ℝm for viscous Hamilton–Jacobi equations. Commun. Part. Differ. Equ. 41 (2016) 1985–2003. [Google Scholar]
  3. C. Bernardini and A. Cesaroni, Ergodic mean-field games with aggregation of Choquard-type. J. Differ. Equ. 364 (2023) 296–335. [Google Scholar]
  4. J.M. Borwein and J.D. Vanderwerff, Convex functions: constructions, characterizations and counterexamples, Vol. 109 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2010). [Google Scholar]
  5. H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 88 (1983) 486–490. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Briani and P. Cardaliaguet, Stable solutions in potential mean field game systems. NoDEA Nonlinear Differ. Equ. Appl. 25 (2018). 10.1007/s00030-017-0493-3 [Google Scholar]
  7. P. Cardaliaguet and P.J. Graber, Mean field games systems of first order. ESAIM Control Optim. Calc. Var. 21 (2015) 690–722. [MathSciNet] [Google Scholar]
  8. P. Cardaliaguet, P.J. Graber, A. Porretta and D. Tonon, Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differ. Equ. Appl. 22 (2015) 1287–1317. [CrossRef] [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. P. Cardaliaguet and A. Porretta, An Introduction to Mean Field Game Theory, Mean Field Games. Lecture Notes in Math., 2281. Fond. CIME/CIME Found. Subser., Springer, Cham (2020) 1–158. [Google Scholar]
  11. A. Cesaroni and M. Cirant, Concentration of ground states in stationary mean-field games systems. Anal. PDE 12 (2019) 737–787. [Google Scholar]
  12. A. Cesaroni and M. Cirant, Introduction to Variational Methods for Viscous Ergodic Mean-field Games with Local coupling. Contemporary Research in Elliptic PDEs and Related Topics. Springer INdAM Ser., 33, Springer, Cham (2019) 221–246. [Google Scholar]
  13. M. Cirant, On the solvability of some ergodic control problems in ℝd. SIAM J. Control Optim. 52 (2014) 4001–4026. [Google Scholar]
  14. M. Cirant, Stationary focusing mean field games. Commun. Part. Differ. Equ. 41 (2016) 1324–1346. [Google Scholar]
  15. M. Cirant, On the existence of oscillating solutions in non-monotone mean-field games. J. Differ. Equ. 266 (2019) 8067–8093. [Google Scholar]
  16. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Vol. 28. SIAM (1976). [Google Scholar]
  17. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin (2001) xiv+517. [Google Scholar]
  18. D.A. Gomes, L. Nurbekyan and M. Prazeres, One-dimensional stationary mean-field games with local coupling. Dyn. Games Appl. 8 (2018) 315–351. [Google Scholar]
  19. D.A. Gomes, S. Patrizi and V. Voskanyan, On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. 99 (2014) 49–79. [Google Scholar]
  20. D.A. Gomes and E. Pimentel, Local regularity for mean-field games in the whole space. Minimax Theory Appl. 1 (2016) 65–82. [MathSciNet] [Google Scholar]
  21. N. Ichihara, The generalized principal eigenvalue for Hamilton—Jacobi–Bellman equations of ergodic type. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015) 623–650. [Google Scholar]
  22. H. Kouhkouh, A viscous ergodic problem with unbounded and measurable ingredients. Part 2. Mean-field games. Preprint arXiv:2311.04616 [Google Scholar]
  23. J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343 (2006) 619–625. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  25. E.H. Lieb, Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Stud. Appl. Math. 57 (1976/1977) 93–105. [Google Scholar]
  26. E.H. Lieb and M. Loss, Analysis, 2nd edn. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI (2001). xxii+346. [Google Scholar]
  27. P.L. Lions, The Choquard equation and related questions. Nonlinear Anal. 4 (1980) 1063–1072. [Google Scholar]
  28. P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I. Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 109–145. [Google Scholar]
  29. G. Metafune, D. Pallara and A. Rhandi, Global properties of invariant measures. J. Funct. Anal. 223 (2005) 396–424. [Google Scholar]
  30. V. Moroz and J. Van Schaftingen, A guide to the Choquard equation. J. Fixed Point Theory Appl. 19 (2019) 773–813. [Google Scholar]
  31. V. Moroz and J. Van Schaftingen, Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J. Funct. Anal. 265 (2013) 153–184. [Google Scholar]
  32. R.T. Rockafellar, Integral Functionals, Normal Integrands and Measurable Selections. Lect. Notes Math. 543, (1976) 157–207. [Google Scholar]
  33. R.L. Wheeden and A. Zygmund, Measure and integral. An introduction to real analysis. Pure and Applied Mathematics, Vol. 43. Marcel Dekker, Inc., New York-Basel, 1977. x+274. [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.