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Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations

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Ukrainian Mathematical Journal Aims and scope

We establish conditions for the existence of an invariant set of the system of differential equations

$$ \frac{{d{\rm{\varphi}} }}{{dt}} = a\left( {\rm{\varphi}} \right),\quad \frac{{dx}}{{dt}} = P\left( {\rm{\varphi}} \right)x + F\left( {{\rm{\varphi}}, x} \right), $$

where a: Φ→Φ, P: Φ→L(X, X), and F: Φ × X→X are continuous mappings and Φ and X are finite-dimensional Banach spaces.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    M. O. Perestyuk

  2. National University of Water Industry and Nature Management, Rivne, Ukraine

    V. Yu. Slyusarchuk

Authors
  1. M. O. Perestyuk
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  2. V. Yu. Slyusarchuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 948–957, July, 2009.

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Perestyuk, M.O., Slyusarchuk, V.Y. Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations. Ukr Math J 61, 1123–1136 (2009). https://doi.org/10.1007/s11253-009-0265-2

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  • DOI: https://doi.org/10.1007/s11253-009-0265-2

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