On the instability of differential systems with varying delay (Q1856856)

The paper is devoted to delay differential systems of the form \[ \dot{x}(t)=A(t)x(t)+B(t)x(t-r_1(t))+f(t,x(t),x(t-r_2(t))), \quad t\geq 0, \tag{1} \] where \(x=(x_1,\ldots,x_n)\), \(f(t,0,0)=0\), the delays \(r_1\) and \(r_2\) are continuous and bounded and \(A(t)\) and \(B(t)\) are continuous matrices. The author extends Coppel's instability theorem [\textit{W. A. Coppel}, J. Lond. Math. Soc. 39, 255-260 (1964; Zbl 0128.08205)] to delay differential systems (1). Several simple illustrative examples are given.