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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the perturbability of the asymptotic manifold of a perturbed system of differential equations


Authors: G. Ladas, V. Lakshmikantham and S. Leela
Journal: Proc. Amer. Math. Soc. 27 (1971), 65-71
MSC: Primary 34.53
DOI: https://doi.org/10.1090/S0002-9939-1971-0274888-3
MathSciNet review: 0274888
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Abstract: We investigate the asymptotic relationship between the solutions of a linear differential system and its perturbed system. Our results depend upon a known result of F. Brauer on asymptotic equilibrium. We also study the asymptotic manifold of solutions of the nonlinear system generated by the solutions of the corresponding linear system.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274888-3
Keywords: Ordinary differential equations, asymptotic manifold, equilibrium, asymptotically equivalent, generalized asymptotically equivalent, perturbed systems
Article copyright: © Copyright 1971 American Mathematical Society