Holomorphic Solutions of Functional Differential Systems Near a Singular Point
Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form (Z^D)*y'(z) = A(z)y(z) + B(z)y(alphaz) + C(z)y'(alphaz) in the neighborhood of the singularity at Z = 0.
L. M. Hall and L. J. Grimm, "Holomorphic Solutions of Functional Differential Systems Near a Singular Point," Proceedings of the American Mathematical Society, American Mathematical Society, Jan 1974.
The definitive version is available at https://doi.org/10.1090/S0002-9939-1974-0328262-4
Mathematics and Statistics
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© 1974 American Mathematical Society, All rights reserved.