Existence theorems for analytic solutions of differential and functional differential equations. (English) Zbl 0685.34066

Existence of distributional solutions of linear ordinary differential equations and linear-differential equations has a great importance in some problems of mathematical physics. Therefore the theory of such solutions has been developed in the last years [for instance see K. L. Cooke and J. Wiener, J. Math. Anal. Appl. 98, 111-129 (1984; Zbl 0527.34069) and J. Wiener, ibid. 88, 170-182 (1982; Zbl 0489.34080)]. Using the classical methods of the Laplace transform and the Taylor’s series the authors prove in the present paper six theorems dealing with the existence and uniqueness of holomorphic and entire solutions of some linear ordinary differential and functional- differential equations.
Reviewer: M.Kisielewicz


34K05 General theory of functional-differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.