Stable recovery of a non-compactly supported coefficient of a Schrödinger equation on an infinite waveguide

We study the stability issue for the inverse problem of determining a coefficient appearing in a Schr\"odinger equation defined on an infinite cylindrical waveguide. More precisely, we prove the stable recovery of some general class of non-compactly and non periodic coefficients appearing in an unbounded cylindrical domain. We consider both results of stability from full and partial boundary measurements associated with the so called Dirichlet-to-Neumann map. To the best of our knowledge, our results are the first results of stable recovery of such class of coefficients for an elliptic equation in an unbounded domain.