On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case

Italo Capuzzo Dolcetta, Andrea Davini

We study the asymptotic behavior of the viscosity solutions $u_G^{\lambda }$ of the Hamilton-Jacobi (HJ) equation \begin{equation*} λu(x)+G(x,u')=c(G)\qquad\hbox{in $\mathbb{R}$} \end{equat…