2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76840Given a separable, locally compact Hausdorff space $X$ and a positive Radon measure $m(dx)$ on it, we study the problem of finding the potential $V(x) \ge 0$ that maximizes the first eigenvalue of the Schrödinger-type operator $L+V(x)$; $L$ is the generator of a local Dirichlet form $(a, D[a])$ on $L^2(X, m(dx))$.15 pages. Accepted for publication on Journal of Functional AnalysisSpectral Theorytext