On relation between uniform asymptotic stability and exponential stability of linear differential equations

On Different Types of Stability for Linear Delay Dynamic Equations

“…This shows that the trivial solution of the pantograph equation ( 44) is globally asymptotically stable by Theorem 2.4 (cf [34,Theorem 2.6]). Consider the two-term equation with both a delay and a non-delay term…”

“…Different types of stability for linear delay differential and difference equations, even with a single delay, continue to attract attention, see, for example, the recent papers [20,34] and references therein. For linear delay equations, the stability type has been connected to properties of the kernels of solution representations [4,8,34].…”

“…Stability and asymptotic stability of the differential equation (2) have been studied in [31,39,40,47], and the exponential stability of (2) in [4,5]. Some results on stability and asymptotic stability of (3) can be found in [18,23,26,33,34,36,37,48,49], and some results on the exponential stability in [6,7,34].…”

Asymptotic properties of neutral type linear systems

“…Are uniform asymptotic stability and uniform exponential stability equivalent for linear neutral systems with bounded delays? For equations without a neutral term this is known [16,21].…”