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Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lya- punov functions and Razumikhin technique.
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Stability and practically stability comparison criteria of impulsive integro-differential systems with fixed moments of impulse effects are established by cone-Lyapunov functions through comparing with impulsive ordinary differential equations.
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In this paper, we investigate the stability of the trivial solution for impulsive functional differential systems using several Lyapunov functions including partial components coupled with the Razumikhin technique, and obtained so...
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In this paper, we investigate the stability of the trivial solution for impulsive functional differential systems using several Lyapunov functions including partial components coupled with the Razumikhin technique, and obtained some new Razumikhin-type theorems which avoid using the auxiliary function P under less restrictive conditions. Our results improve some of the earlier findings, and are suitable for many applications. Some examples are given to illustrate the advantages of the theorems obtained. (c) 2006 Elsevier Ltd. All rights reserved.
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In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of t...
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In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov-Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations.
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This paper studies the W-stability of the solutions of nonlinear impulsive functional differential systems by using Lyapunov functions and Razumikhin technique. Some results that guarantee the W-stability and W-uniform stability a...
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This paper studies the W-stability of the solutions of nonlinear impulsive functional differential systems by using Lyapunov functions and Razumikhin technique. Some results that guarantee the W-stability and W-uniform stability are obtained here. And the asymptotical stability criteria of nonlinear impulsive functional differential systems are then established by using the W-uniform stability, which show the advantages of the obtained results. (C) 2007 Elsevier B.V. All fights reserved.
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This paper is devoted to studying the ultimate boundedness of impulsive stochastic delay differential equations (SDDEs) with delayed impulses. Using suitable Lyapunov functionals and Ito's formula, some necessary criteria are met ...
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This paper is devoted to studying the ultimate boundedness of impulsive stochastic delay differential equations (SDDEs) with delayed impulses. Using suitable Lyapunov functionals and Ito's formula, some necessary criteria are met to guarantee the system's pth moment global exponential ultimate boundedness (p-MGEUB). The results show that the unbounded stochastic delay differential equation can be transformed into a bounded system by impulses. Moreover, our results generalize and improve some results in the literature. Finally, we provide an illustration to clarify our findings.(c) 2023 Elsevier B.V. All rights reserved.
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In this note, we study the exponential stability of impulsive functional differential systems with infinite delays by using the Razumikhin technique and Lyapunov functions. Several Razumikhin-type theorems on exponential stability...
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In this note, we study the exponential stability of impulsive functional differential systems with infinite delays by using the Razumikhin technique and Lyapunov functions. Several Razumikhin-type theorems on exponential stability are obtained, which shows that certain impulsive perturbations may make unstable systems exponentially stable. Some examples are discussed to illustrate our results. (C) 2008 Published by Elsevier B.V.
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This paper concerns with the ultimate boundedness problem for impulsive fractional delay differential equations. Based on the impulsive fractional differential inequality, the boundedness of Mittag-Leffler functions, and the succe...
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This paper concerns with the ultimate boundedness problem for impulsive fractional delay differential equations. Based on the impulsive fractional differential inequality, the boundedness of Mittag-Leffler functions, and the successful construction of suitable Lyapunov functionals, some algebraic criteria are derived for testing the global ultimate boundedness of the equations, and the estimations of the global attractive sets are provided as well. One example is also given to show the effectiveness of the obtained theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.
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Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro- differential equations with and without constant retardation are investigated using a new type of Lyapunov- Krasovskii funct...
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Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro- differential equations with and without constant retardation are investigated using a new type of Lyapunov- Krasovskii functionals. An advantage of the new functionals used here is that they eliminate using Gronwall's inequality. Compared to related results in the literature, the conditions here are more general, simple, and convenient to apply. Examples to show the application of the theorems are included.
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In this paper, an impulsive integro-differential equation is considered. By establishing an integro-differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius...
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In this paper, an impulsive integro-differential equation is considered. By establishing an integro-differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, some new sufficient conditions for global exponential stability of impulsive inteuro-differential equation are obtained. The results extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the theory. (c) 2005 Elsevier Ltd. All rights reserved.
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