On a local theory of asymptotic integration for nonlinear ordinary differential equations
Mustafa, Octavian G.
Agarwal, Ravi P.
By 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.
Mathematics - Classical Analysis and ODEs, Mathematics - Dynamical Systems, 34E05, 34A45