Stability under Persistent Disturbances of Impulsive Differential-Difference Equations of Neutral Type

Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

“…We get 8 = 8(e) > 0 such that b(8) < a(e). Let (p 0 6 D : Hvoll < 8 and x(t) =x(t;t 0 , <p 0 ) be the solution of the initial value problem (1), (2).…”

“…A natural generalization of impulsive ordinary differential equations is impulsive functional-differential equations. In spite of the great possibilities for applications, the theory of these equations is developing rather slowly due to a series of difficulties of technical and theoretical character [1][2][3].…”

On the asymptotic stability for impulsive functional differential equations

“…In recent years, significant progress has been made in the stability theory of systems of impulsive functional differential equations [1][2][3][14][15][16]. As we can see in these references, there are some difficulties one must face in developing the corresponding stability theory of impulsive functional differential equations.…”

“…Recently, the number of publications dedicated to the investigation of stability grows constantly and has taken shape of a developed theory, and some asymptotic (uniform asymptotic) stability theorems for the system (1.1) have been obtained, see, for example [1][2][3]15,16] where the negative definite property of the derivative V along a solution of (1.1) was required. However, to the best knowledge of the authors, few publications are dedicated to this subject in which the derivative V is required to be negative definite only on a sequence of intervals of [0, ∞).…”

Positive periodic solutions for a neutral impulsive delayed Lotka–Volterra competition system with the effect of toxic substance

“…Remark 2. We assume (H 6 ) in Theorem 3.1 and (H 7 )in Theorem 3.2 in the present paper, corresponding to condition (H 4 ) of Theorem 3.1 (or Theorem 3.2) in[2,23], they only assume…”