Rus, Ioan A. Ulam stabilities of ordinary differential equations in a Banach space. (English) Zbl 1224.34164 Carpathian J. Math. 26, No. 1, 103-107 (2010). Four types of Ulam stability for the following differential equation in a Banach space \(\mathbb B\) are considered: \[ u'(t)=Au(t)+f(t,u(t)),\;t\in I\subset\mathbb R, \] where \(A\) is the infinitesimal generator of a \(C_0\)-semigroup, \(f\in C(I\times\mathbb B,\mathbb B)\). In the case of a compact interval \(I\), the author proves Ulam-Hyers stability for the considered equation, assuming that \(f\) is Lipschitzian in the second variable. Moreover, in the case \(I=[a,+\infty)\), generalized Ulam-Hyers-Rassias stability with respect to an increasing function \(\varphi\in C(I,\mathbb R_+)\) is established. Reviewer: Ovidiu Carja (Iasi) Cited in 156 Documents MSC: 34D10 Perturbations of ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces Keywords:ordinary differential equations; Ulam-Hyers stability; Ulam-Hyers-Rassias stability PDFBibTeX XMLCite \textit{I. A. Rus}, Carpathian J. Math. 26, No. 1, 103--107 (2010; Zbl 1224.34164)