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Limit-periodic solutions of integro-differential equations in a critical case

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Abstract

We consider equations with nonlinear terms representable by power series in the variable and functionals in integral form. The equation depends on a small exponentially limitperiodic perturbation, i.e., on a function that exponentially tends to a periodic function as the independent variable increases. In the Lyapunov critical case of one zero root, we prove the existence of a family of exponentially limit-periodic solutions of the equation in the form of power series in the small parameter and arbitrary initial values of the noncritical variables.

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Authors and Affiliations

  1. Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, 119333, Russia

    V. S. Sergeev

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  1. V. S. Sergeev
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Correspondence to V. S. Sergeev.

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Original Russian Text © V.S. Sergeev, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 9, pp. 1232–1241.

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Sergeev, V.S. Limit-periodic solutions of integro-differential equations in a critical case. Diff Equat 53, 1197–1206 (2017). https://doi.org/10.1134/S0012266117090099

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