Khusainov, D. Ya.; Shuklin, G. V. Linear autonomous time-delay system with permutation matrices solving. (English) Zbl 1064.34042 Stud. Univ. Žilina, Math. Ser. 17, No. 1, 101-108 (2003). The authors study the existence of solutions of the inhomogeneous delay equation \[ x'(t)=Ax(t)+Bx(t-\tau)+f(t),\quad t\geq 0,\;x(t)=\varphi (t),\;-\tau\leq t\leq 0. \] Assuming that the matrices \(A\) and \(B\) commute, they can write the solutions of this equation in terms of the so-called delayed exponential, the solution of the differential equation with pure delay \[ x'(t)=Bx(t-\tau),\quad t \geq 0,\;x(t)=\varphi(t),\quad -\tau\leq t\leq 0, \] studied before by the authors. Reviewer: Lahcen Maniar (Marrakech) Cited in 1 ReviewCited in 71 Documents MSC: 34K06 Linear functional-differential equations Keywords:delay equation; delayed exponential PDFBibTeX XMLCite \textit{D. Ya. Khusainov} and \textit{G. V. Shuklin}, Stud. Univ. Žilina, Math. Ser. 17, No. 1, 101--108 (2003; Zbl 1064.34042)