Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices

Sufficient conditions for the exponential stability of the trivial solution of nonlinear differential equations with delay and with linear parts of the form Ax(t)+Bx(t−τ),τ>0Ax(t)+Bx(t−τ),τ>0, where AB=BAAB=BA, are proved. A result on the nonexistence of blowing-up solutions is also proved.