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On the Ulam stability of a class of Banach space valued linear differential equations of second order. (English) Zbl 1417.34141
Summary: Let \(E\) be a complex Banach space. We prove the Ulam stability of a class of Banach space valued second order linear differential equations \(p(x)y'' (x) + q(x)y' (x) + \lambda y(x) = 0\), where \(p \in C^1 [I, \mathbb R ^+]\), \(q \in C[I, \mathbb R]\) with \(p' (x) = 2q(x)\) for each \(x \in I\); \(I\) denotes an open interval in \(\mathbb R\), \(\lambda\) is a fixed positive real number. Moreover, we also provide some applications of our results.

MSC:
34G10 Linear differential equations in abstract spaces
34D20 Stability of solutions to ordinary differential equations
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