Published in Journal of Differential Equations, 2025
Recommended citation: H. Mitake, P. Ni, Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems, Journal of Differential Equations 440 (2025) 113442.
Published in Mathematische Zeitschrift, 2025
Recommended citation: P. Ni, M. Zavidovique, Nonlinear and degenerate discounted approximation in discrete weak KAM theory, Mathematische Zeitschrift (2025) 310:63.
Published in Journal of Differential Equations, 2024
Recommended citation: P. Ni, Time periodic solutions of first order mean field games from the perspective of Mather theory, J. Differential Equations, 412 (2024), 881-901.
Published in Communications on Pure and Applied Analysis, 2024
Recommended citation: P. Ni, Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step, Comm. Pure Appl. Anal., 23 (2024), 961-983.
Published in Journal of Differential Equations, 2024
Recommended citation: P. Ni, L. Wang, A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited, J. Differential Equations, 403 (2024), 272 – 307.
Published in SCIENCE CHINA Mathematics, 2023
This paper is about the topological dynamics of the Aubry sets for contact Hamiltonian systems.
Recommended citation: P. Ni and L. Wang, Aubry-Mather theory for contact Hamiltonian systems III, SCIENCE CHINA Mathematics, published online, 2023. https://www.sciengine.com/SCM/doi/10.1007/s11425-022-2197-4
Published in Chinese Annals of Mathematics, Series B, 2023
This paper is about the implicit solution semigroup for the standard PDE assumptions.
Recommended citation: P. Ni, L. Wang, and J. Yan, A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its applications, Chinese Annals of Mathematics, Series B, to appear. https://arxiv.org/abs/2101.00446
Published in Proceedings of the American Mathematical Society, 2023
This paper is about a counter example for vanishing discount problem when the Hamiltonian is non-monotone in the unknown function.
Recommended citation: P. Ni, Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem, Proc. Amer. Math. Soc. 151 (2023), 5239-5250. https://doi.org/10.1090/proc/16420
Published in Communications on Pure and Applied Analysis, 2023
This paper is about H-J equations with the Hamiltonian periodic in the unknown function.
Recommended citation: P. Ni, K. Wang and J. Yan, Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions, Comm. Pure Appl. Anal., 22 (2023), 668-685. https://www.aimsciences.org//article/doi/10.3934/cpaa.2023005
Published in Proceedings of the American Mathematical Society, 2022
This paper is about a weakly coupled mean field games model of first order for k groups of major players.
Recommended citation: P. Ni, K. Wang, and J. Yan, A weakly coupled mean field games model of first order for k groups of major players, Proc. Amer. Math. Soc., published online. https://www.ams.org/journals/proc/earlyview/#proc16342