2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226251By revisiting an asymptotic integration theory of nonlinear ordinary differential equations due to J.K. Hale and N. Onuchic [Contributions Differential Equations 2 (1963), 61--75], we improve and generalize several recent results in the literature. As an application, we study the existence of bounded positive solutions to a large class of semi-linear elliptic partial differential equations via the subsolution-supersolution approach.Classical Analysis and ODEsDynamical Systems34E05; 34A45text