Kalas, Josef Asymptotic properties of an unstable two-dimensional differential system with delay. (English) Zbl 1114.34058 Math. Bohem. 131, No. 3, 305-319 (2006). Summary: The asymptotic behaviour of the solutions is studied for the real unstable two-dimensional system \[ x'(t)={\mathbf A}(t)x(t)+{\mathbf B}(t)x(t-r)+h(t,x(t),x(t-r)), \]where \(r>0\) is a constant delay. It is supposed that \(\mathbf A\), \(\mathbf {B}\) and \(h\) are matrix functions and a vector function, respectively. The method of investigation is based on the transformation of the real system into an equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by means of Ważewski’s topological principle. Cited in 3 Documents MSC: 34K25 Asymptotic theory of functional-differential equations Keywords:delayed differential equation; asymptotic behaviour; boundedness of solutions; Lyapunov method PDFBibTeX XMLCite \textit{J. Kalas}, Math. Bohem. 131, No. 3, 305--319 (2006; Zbl 1114.34058) Full Text: EuDML Link