Stability results for impulsive functional differential equations with infinite delays (original) (raw)
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Strict Stability Criteria for Impulsive Functional Differential Equations
Strict stability is the kind of stability that can give us some information about the rate of decay of the solution. There are some results about strict stability of functional differential equations. In this paper, we shall extend strict stability to Impulsive functional differential equations in which the state variables on the impulses are related to time delay. By using Lyapunov functions and Razumikhin technique, some criteria for strict stability for functional differential equations, in which the state variables on the impulses are related to the time delay are provided, and we can see that impulses do contribute to the system's strict stability behavior.
Journal of Mathematical Analysis and Applications, 2006
In this paper, we discuss local and global existence and uniqueness results for first-order impulsive functional differential equations with multiple delay. We shall rely on a fixed point theorem of Schaefer and a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray-Schauder type in Fréchet spaces, due to Frigon and Granas [M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161-168].
Australian Journal of Mathematical Analysis and Applications, 2007
In this paper, we discuss local and global existence and uniqueness results for first-order impulsive functional differential equations with multiple delay. We shall rely on a fixed point theorem of Schaefer and a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray-Schauder type in Fréchet spaces, due to Frigon and Granas [M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161-168].
Differential Equations & Applications, 2009
In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical consequences are derived for the sub-linear growth cases. And an example is also given to illustrate our main results.
Stability of Impulsive Functional Differential Equations via Lyapunov Functionals
International Journal of Mathematics Trends and Technology, 2016
System of differential equations with impulse effect are an adequate apparatus for mathematical simulation of a number of processes and phenomena in science and technology. Recently the number of publications dedicated to their investigation for stability grows constantly and has taken shape of a developed theory presented in monographs [1-3]. Systems of functional differential equations have been much less studied.
On Functionally Equivalent Impulsive Delay Differential Equations
Abstract By means of certain functional relations, the equivalence of impulsive delay differential equations and impulsive differential equations is established. Based on some well known results for impulsive differential equations and for delay differential equations, nontrivial consequences on existence and nonexistence of periodic solutions of impulsive delay differential equations are obtained. Key words: Impulse, Delay, Periodic solutions, Functional equivalence.