Given a continuous Hamiltonian H:(x, p, u)↦ H (x, p, u) defined on T⁎ M× R, where M is a
closed connected manifold, we study viscosity solutions, u λ: M→ R, of discounted …

We study the asymptotic behavior of the viscosity solutions u G λ of the Hamilton-Jacobi (HJ)
equation λ u (x)+ G (x, u′)= c (G) in R as the positive discount factor λ tends to 0, where G …

The aim of these notes is to present a self contained account of discrete weak KAM theory.
Put aside the intrinsic elegance of this theory, it is also a toy model for classical weak KAM …

Motivated by the vanishing contact problem, we study in the present paper the convergence
of solutions of Hamilton–Jacobi equations depending nonlinearly on the unknown function …

We study the asymptotic behavior of solutions of an equation of the form\begin
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …

Consider the generalized discounted Hamilton-Jacobi equation\[\lambda a (x) u+ H (x, Du)=
c (H),\] where $ a (x) $ may vanish or change the signs. Two examples are given in this …

Abstract We study the Hamilton–Jacobi equations H (x, D u, u)= 0 in M and∂ u/∂ t+ H (x, D
xu, u)= 0 in M×(0,∞), where the Hamiltonian H= H (x, p, u) depends Lipschitz continuously …

By exploiting the contact Hamiltonian dynamics (T* M× ℝ, Φ t) around the Aubry set of
contact Hamiltonian systems, we provide a relation among the Mather set, the Φ t-recurrent …

This paper studies a perturbation problem given by the equation:\begin {equation*} H (x,
d_xu_\lambda,\lambda u_\lambda (x))+\lambda V (x,\lambda)= c\quad\text {in $ M $},\end …

Suppose M is a closed Riemannian manifold. For a C 2 generic (in the sense of Mañé)
Tonelli Hamiltonian H: T∗ M→ R, the minimal viscosity solution u λ-: M→ R of the negative …