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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Holomorphic solutions of functional differential systems near singular points


Authors: L. J. Grimm and L. M. Hall
Journal: Proc. Amer. Math. Soc. 42 (1974), 167-170
MSC: Primary 34K05
MathSciNet review: 0328262
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Abstract: 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(\alpha z) + C(z)y'(\alpha z)$ in the neighborhood of the singularity at $ z = 0$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0328262-4
PII: S 0002-9939(1974)0328262-4
Article copyright: © Copyright 1974 American Mathematical Society