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Zbl 1125.34328
Jung, S.-M.
Hyers-Ulam stability of linear differential equations of first order. II.
(English)
[J] Appl. Math. Lett. 19, No. 9, 854-858 (2006). ISSN 0893-9659

Summary: Let $X$ be a complex Banach space and let $I$ be an open interval. For given functions $g : I \rightarrow \Bbb C,\ h : I \rightarrow X$ and $\varphi : I \rightarrow [0,\infty )$, we will solve the differential inequality $\Vert y^{\prime}(t) + g(t)y(t)+h(t)\Vert \leq \varphi (t)$ for the class of continuously differentiable functions $y : I \rightarrow X$ under some integrability conditions. Part I, cf. Appl. Math. Lett. 17, No. 10, 1135--1140 (2004; Zbl 1061.34039); Part III, cf. J. Math. Anal. Appl. 311, No. 1, 139--146 (2005; Zbl 1087.34534).
MSC 2000:
*34G10 Linear ODE in abstract spaces
34A40 Differential inequalities (ODE)

Keywords: Hyers-Ulam stability; Hyers-Ulam-Rassias stability; differential equation

Citations: Zbl 1087.34534; Zbl 1061.34039

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