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The Asymptotic Behavior of a Class of Nonlinear Differential Equations

Cohen, Donald S. (1967) The Asymptotic Behavior of a Class of Nonlinear Differential Equations. Proceedings of the American Mathematical Society, 18 (4). pp. 607-609. ISSN 0002-9939. https://resolver.caltech.edu/CaltechAUTHORS:20200114-141950464

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Abstract

We shall study the asymptotic behavior for t → ∞ of solutions of the following nonlinear differential equation: (1) u” + f(t, u) = 0. We suppose that f(t, u) satisfies the following conditions: H-1: f(t, u) is continuous in D : t ≥ 0, - ∞ < u < ∞. H-2: The derivative of f_u exists on D and satisfies f_u(t, u) > 0 on D. H-3: |f(t, u(t))| ≤ f_u(t, 0) | u(t) | on D.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.2307/2035424DOIArticle
https://www.jstor.org/stable/2035424JSTORArticle
Additional Information:© 1967 American Mathematical Society. Received by the editors October 5, 1966. This work was supported by the National Science Foundation under Grant No. GP-4597 at the California Institute of Technology.
Funders:
Funding AgencyGrant Number
NSFGP-4597
Issue or Number:4
Record Number:CaltechAUTHORS:20200114-141950464
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200114-141950464
Official Citation:Cohen, Donald S. “The Asymptotic Behavior of a Class of Nonlinear Differential Equations.” Proceedings of the American Mathematical Society, vol. 18, no. 4, 1967, pp. 607–609. JSTOR, www.jstor.org/stable/2035424.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100720
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Jan 2020 22:35
Last Modified:14 Jan 2020 22:35

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