Ukrainian Mathematical Journal

, Volume 48, Issue 3, pp 471–474 | Cite as

On the existence of an invariant manifold for weakly nonlinear matrix differential equations

  • V. V. Lipchan
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Abstract

For a system of nonlinear matrix differential equations with small parameter, we establish conditions of the existence of an invariant manifold in terms of the Green function.

Keywords

Banach Space Green Function Nonlinear Oscillation Invariant Manifold Continuous Dependence 

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References

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    A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987),English translation: Kluwer AP, Dordrecht-Boston-London (1991).Google Scholar
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    N. N. Bogolyubov and Yu. A. Mitropol’skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow 1974.MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. V. Lipchan

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