Adesina, Olufemi Adeyinka On the exponential stability of a certain Lurie system. (English) Zbl 1091.34534 Kragujevac J. Math. 26, 73-81 (2004). The author gives some necessary and sufficient conditions which ensure the existence of a bounded solution, which is globally exponentially stable and periodic (or almost-periodic) for some systems. For example, it is considered the following system \[ \frac{dx}{dt}=Ax-bf(\sigma)+P(t),\qquad \sigma=c^Tx, \] where \(c,b\in \mathbb{R}^n,\) \(P(t)\) is bounded, \(A\) a special upper triangular matrix, \(f\) is continuous and \(f(0)=0,\) which is a special Lurie system. Reviewer: Stevo Stević (Beograd) MSC: 34D23 Global stability of solutions to ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:globally asymptotically stable solution; periodic solution; bounded solution PDFBibTeX XMLCite \textit{O. A. Adesina}, Kragujevac J. Math. 26, 73--81 (2004; Zbl 1091.34534)