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Global analyticity of solutions of nonlinear functional differential equations representable by Dirichlet series

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Abstract

We show that, under certain additional assumptions, analytic solutions of sufficiently general nonlinear functional differential equations are representable by Dirichlet series of unique structure on the entire real axis ℝ and, in some cases, on the entire complex plane ℂ. We investigate the dependence of these solutions on the coefficients of the basic exponents of the expansion into a Dirichlet series. We obtain sufficient conditions for the representability of solutions of the main initial-value problem by series of exponents.

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Authors and Affiliations

  1. Moscow State Automobile-and-Road Technical University, Moscow, Russia

    A. N. Murovtsev

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  1. A. N. Murovtsev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1276–1284, September, 2006.

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Murovtsev, A.N. Global analyticity of solutions of nonlinear functional differential equations representable by Dirichlet series. Ukr Math J 58, 1448–1457 (2006). https://doi.org/10.1007/s11253-006-0144-z

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  • DOI: https://doi.org/10.1007/s11253-006-0144-z

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