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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 23
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 4, August 2016
  4. Nonlinear elliptic systems and mean-field games
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 5, October 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 4, August 2016
The bang–bang theorem via Baire category: a dual approach
Pucci eigenvalues on geodesic balls
Three solutions for a class of higher dimensional singular problems
On noncoercive elliptic problems
Fully nonlinear operators with Hamiltonian: Hölder regularity of the gradient
Calderón–Zygmund estimates for a class of obstacle problems with nonstandard growth
Existence of infinitely many solutions for the (p, q)-Laplace equation
Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues
The ergodic problem for some subelliptic operators with unbounded coefficients
Local well-posedness for the (n + 1)-dimensional Yang–Mills and Yang–Mills–Higgs system in temporal gauge
Nonlinear elliptic systems and mean-field games
Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 3, June 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 2, April 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 1, February 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Nonlinear elliptic systems and mean-field games

Content Provider SpringerLink
Author Bardi, Marti Feleqi, Ermal
Copyright Year 2016
Abstract We consider a class of quasilinear elliptic systems of PDEs consisting of N Hamilton–Jacobi–Bellman equations coupled with N divergence form equations, generalising to N > 1 populations the PDEs for stationary Mean-Field Games first proposed by Lasry and Lions. We provide a wide range of sufficient conditions for the existence of solutions to these systems: either the Hamiltonians are required to behave at most linearly for large gradients, as it occurs when the controls of the agents are bounded, or they must grow faster than linearly and not oscillate too much in the space variables, in a suitable sense. We show the connection of these systems with the classical strongly coupled systems of Hamilton–Jacobi–Bellman equations of the theory of N-person stochastic differential games studied by Bensoussan and Frehse. We also prove the existence of Nash equilibria in feedback form for some N-person games.
Ending Page 32
Page Count 32
Starting Page 1
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 23
Language English
Publisher Springer International Publishing
Publisher Date 2016-07-27
Publisher Place Cham
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword N-person games Noncooperative games Nash equilibria Nonlinear elliptic systems Analysis Differential games PDEs in connection with game theory, economics, social and behavioral sciences Mean-Field Games Stochastic differential games
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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