Stability of nonautonomous difference equations with several delays
The authors study the stability of solutions of the difference equation \[ x(n+1)-x(n)=-\sum\limits^K_{k=0} a_k(n) x(n-h_k(n)), \quad n \geq m, \quad m \in {\mathbb N}_0, \eqno(1) \] where \({\mathbb N}_0 = {\mathbb N} \cup \{0\}\), \(a_k: {\mathbb N}_0 \to {\mathbb R}\), \(h_k: {\mathbb N}_0 \to {\mathbb N}_0\), \(k =0, \dots, K\), \(x(i) = 0\) for \(i < m\). They associate (1) with the following delay equation \[ y'(t) = - \sum\limits^K_{k=0} a_k([t]) y([t]-h_k([t])), \quad t \in {\mathbb R}_+, \] where \([t]\) is the integer part of \(t\). Using the known results for this equation the authors obtain analogous theorems for (1). Some illustrative examples are given and a comparative analysis with the known assertions for (1) is conducted.
scientific article; zbMATH DE number 5533458