2017
Том 69
№ 9

All Issues

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

Murovtsev A. N.

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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 $\mathbb{R}$ and, in some cases, on the entire complex plane $\mathbb{C}$. 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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 9, pp 1448-1457.

Citation Example: Murovtsev A. N. Global analyticity of solutions of nonlinear functional differential equations representable by Dirichlet series // Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1276–1284.

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