On a local theory of asymptotic integration for nonlinear ordinary differential equations

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Mustafa, Octavian G.
Agarwal, Ravi P.
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Abstract
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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.
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Mathematics - Classical Analysis and ODEs, Mathematics - Dynamical Systems, 34E05, 34A45
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