Malygina, V. V.; Kulikov, A. Y. On precision of constants in some theorems on stability of difference equations. (English) Zbl 1153.39003 Funct. Differ. Equ. 15, No. 3-4, 239-248 (2008). The authors study stability conditions (uniform and asymptotic stability) for the linear difference equation \[ x(n+1)-x(n)=-a(n)\,x(n-h(n)), \quad n\in{\mathbb N}_0. \tag{\(*\)} \]More precisely, they show that the conditions \[ a(n)\geq0 \quad\text{and}\quad \sup_{n\in{\mathbb N}_0}\,\sum_{i=n-h(n)}^n a(i)\leq\frac{3}{2} \] imply the uniform stability of equation (\(*\)). A large part of the paper is devoted to showing that the constant \(\frac{3}{2}\) above as well as other constants such as \(\frac{3}{2}+\frac{1}{2k+1}\) in similar results in the literature are sharp. Reviewer: Roman Šimon Hilscher (Brno) Cited in 6 Documents MSC: 39A10 Additive difference equations 39A11 Stability of difference equations (MSC2000) Keywords:functional difference equation; uniform stability; asymptotic stability; linear difference equation PDFBibTeX XMLCite \textit{V. V. Malygina} and \textit{A. Y. Kulikov}, Funct. Differ. Equ. 15, No. 3--4, 239--248 (2008; Zbl 1153.39003)