Hyers-Ulam stability of linear differential operator with constant coefficients

被引：101
|
作者：
Miura, T [1 ]
Miyajima, S
Takahasi, SE
机构：
[1] Yamagata Univ, Dept Basic Technol Appl Math & Phys, Yonezawa, Yamagata 9928510, Japan
[2] Sci Univ Tokyo, Fac Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan
来源：
MATHEMATISCHE NACHRICHTEN | 2003年 / 258卷
关键词：
Hyers-Ulam stability; n-th order linear differential operator; exponential functions;
D O I：
10.1002/mana.200310088
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let P(z) be a polynomial of degree n with complex coefficients and consider the n-th order linear differential operator P(D). We show that the equation _P(D)f = 0 has the Hyers-Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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页码：90 / 96
页数：7
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