4 papers
On the inhomogeneous discounted Hamilton-Jacobi equations
Liang Jin, Jun Yan, Kai Zhao
In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{} \end{equation} on a clo…
On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits
Liang Jin, Jun Yan, Kai Zhao
This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \cite{JY}, but without monotonicity assumption. Due to the complexity of general cases,…
Dynamics of globally minimizing orbits in contact Hamiltonian systems
Yang Xu, Jun Yan, Kai Zhao
In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the -limit set of globally m…
Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
Andrea Davini, Panrui Ni, Jun Yan +1
We study the asymptotic behavior of solutions of an equation of the form \begin{equation}\label{abs}\tag{*} G\big(x, D_x u,λu(x)\big) = c_0\qquad\hbox{in } \end{equation} on a…