Ulam's problem for approximate homomorphisms in connection with Bernoulli's differential equation
\textit{C. Alsina} and \textit{R. Ger} [J. Inequal. Appl. 2, No. 4, 373--380 (1998; Zbl 0918.39009)] proved the Hyers-Ulam stability of the differential equation \(y'(t)=y(t)\). Their result was generalized by \textit{S.-E. Takahasi, T. Miura} and \textit{S. Miyajima} [Bull. Korean Math. Soc. 39, No. 2, 309--315 (2002; Zbl 1011.34046)]. \textit{S.-M. Jung} [Appl. Math. Lett. 17, No. 10, 1135--1140 (2004; Zbl 1061.34039)] investigated the stability of \(a(t)y'(t)=y(t)\). In the paper under review, the authors nicely prove the generalized Hyers-Ulam stability of the Bernoulli differential equation \(y(t)^{-\alpha}y'(t)+g(t)y(t)^{1-\alpha}+h(t)=0\), where \(g\) and \(h\) are given continuous functions and \(\alpha \neq 1\) is a fixed real number.
scientific article; zbMATH DE number 5163926