# Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients

Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous... In this article, we investigate Gevrey and summability properties of formal power series solutions of certain classes of inhomogeneous linear integro-differential equations with analytic coefficients in a neighborhood of ( 0 , 0 ) ∈ ℂ 2 $(0,0)\in \mathbb {C}^{2}$ . In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient positive rational number k, in a given direction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Dynamical and Control Systems Springer Journals

# Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients

, Volume 23 (4) – Jul 12, 2017
26 pages
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/lp/springer_journal/gevrey-order-and-summability-of-formal-series-solutions-of-certain-myXD7BoUTS
Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Engineering; Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control
ISSN
1079-2724
eISSN
1573-8698
D.O.I.
10.1007/s10883-017-9371-x
Publisher site
See Article on Publisher Site

### Abstract

In this article, we investigate Gevrey and summability properties of formal power series solutions of certain classes of inhomogeneous linear integro-differential equations with analytic coefficients in a neighborhood of ( 0 , 0 ) ∈ ℂ 2 $(0,0)\in \mathbb {C}^{2}$ . In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient positive rational number k, in a given direction.

### Journal

Journal of Dynamical and Control SystemsSpringer Journals

Published: Jul 12, 2017

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