Stability of solutions of linear delay differential equations
Date of Original Version
Consider the linear differential equation x(t)= Σi=1npi(t)x(t-ti)=0, t≥t0where p C([t0∞), R) and ti>0 for i = 1, 2,…, n. By investigating the asymptotic behavior first of the nonoscillatory solutions of (1) and then of the oscillatory solutions we are led to new sufficient conditions for the asymptotic stability of the trivial solution of (1). When the coefficients of (1) are all of the same sign, we obtain a comparison result which shows that the nonoscillatory solutions of (1) dominate the growth of the oscillatory solutions. © 1987 American Mathematical Society.
Proceedings of the American Mathematical Society
Kulenović, M. R.S., G. Ladas, and A. Meimaridou. "Stability of solutions of linear delay differential equations." Proceedings of the American Mathematical Society 100, 3 (1987): 433-441. doi:10.1090/S0002-9939-1987-0891141-7.