Andrea Davini

Vanishing discount selection for constant-sign local perturbations of periodic Hamiltonians

We study the vanishing discount selection problem for critical Hamil\-ton--Jacobi equations posed on ${\mathbb R}^d$ with Hamiltonian $G=H-V$, where $H$ is continuous, periodic in space, convex and superlinear in the momentum, and $V$ is a compactly supported potential of constant sign. For $V\leqslant0$, we prove loca...