2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112887We find an asymptotics on the diagonal of the Green function of a Sturm-Liouville operator and give its applications for Riccati equation.31 pages. The shortened version of this paper is to be submitted to Journal of Mathematical Analysis and ApplicationsClassical Analysis and ODEs34B24; 34B27; 34B30; 34E99text