an:06970582
Zbl 1417.34141
Shen, Yonghong; Chen, Wei; Lan, Yaoyao
On the Ulam stability of a class of Banach space valued linear differential equations of second order
EN
Adv. Difference Equ. 2014, Paper No. 294, 9 p. (2014).
00358588
2014
j
34G10 34D20
Ulam stability; linear differential equation; Chebyshev differential equation; Banach space
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.