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

被引：14
|
作者：
Remy, Pascal [1 ]
机构：
[1] Lycee Les Pierres Vives, 1 Rue Alouettes, F-78420 Carrieres Sur Seine, France
来源：
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2017年 / 23卷 / 04期
关键词：
Linear integro-differential equation; Divergent power series; Newton polygon; Gevrey order; Summability; PARTIAL-DIFFERENTIAL-EQUATIONS; BOREL SUMMABILITY; DIVERGENT SOLUTIONS; STOKES PHENOMENON; NEWTON POLYGONS; HEAT-EQUATION; MULTISUMMABILITY;
D O I：
10.1007/s10883-017-9371-x
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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) is an element of 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.
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页码：853 / 878
页数：26
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