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Singular-perturbation method for nonlinear second-order evolution inclusions with Volterra operators

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Nonlinear Oscillations

We consider a class of second-order operator differential inclusions with Volterra-type operators. Using the singular-perturbation method, we study the problem of the existence of a solution of the Cauchy problem for these inclusions. Important a priori estimates are obtained for solutions and their derivatives. We give an example that illustrates the proposed approach to the analysis of the problem under consideration.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    N. V. Zadoyanchuk & P. O. Kas’yanov

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  1. N. V. Zadoyanchuk
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  2. P. O. Kas’yanov
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Correspondence to N. V. Zadoyanchuk.

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Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 27–43, January–March, 2009.

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Zadoyanchuk, N.V., Kas’yanov, P.O. Singular-perturbation method for nonlinear second-order evolution inclusions with Volterra operators. Nonlinear Oscill 12, 27–44 (2009). https://doi.org/10.1007/s11072-009-0057-5

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  • DOI: https://doi.org/10.1007/s11072-009-0057-5

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