Hyers-Ulam stability of linear differential equations of first order. II. (English) Zbl 1125.34328

Summary: Let \(X\) be a complex Banach space and let \(I\) be an open interval. For given functions \(g : I \rightarrow \mathbb C,\;h : I \rightarrow X\) and \(\varphi : I \rightarrow [0,\infty )\), we will solve the differential inequality \(\| y^{\prime}(t) + g(t)y(t)+h(t)\| \leq \varphi (t)\) 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).


34G10 Linear differential equations in abstract spaces
34A40 Differential inequalities involving functions of a single real variable
Full Text: DOI


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