2019
Том 71
№ 11

All Issues

Murovtsev A. N.

Articles: 1
Brief Communications (Russian)

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

Murovtsev A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1276–1284

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.