References
- D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1989.
- S. K. Choi and N. Koo, Variationally stable impulsive differential systems, Dyn. Syst. 30 (2015), no. 4, 435-449. https://doi.org/10.1080/14689367.2015.1068742
- S. K. Choi and N. Koo, A converse theorem on h-stability via impulsive variational systems, J. Korean Math. Soc. 53 (2016), no. 5, 1115-1131. https://doi.org/10.4134/JKMS.j150428
- F. M. Dannan and S. Elaydi, Lipschitz stability of nonlinear systems of differential equations, J. Math. Anal. Appl. 113 (1986), no. 2, 562-577. https://doi.org/10.1016/0022-247X(86)90325-2
- B. Ghanmi, On the practical h-stability of nonlinear systems of differential equations, J. Dyn. Control Syst. 25 (2019), no. 4, 691-713. https://doi.org/10.1007/s10883-019-09454-5
- B. Ghanmi, Partial stability analysis of nonlinear time-varying impulsive systems, Int. J. Biomath. 12 (2019), no. 6, 1950066, 26 pp. https://doi.org/10.1142/S1793524519500669
- B. Ghanmi, M. Dlala, and M. A. Hammami, Converse theorem for practical stability of nonlinear impulsive systems and applications, Kybernetika (Prague) 54 (2018), no. 3, 496-521. https://doi.org/10.14736/kyb-2018-3-0496
- X. Hao and L. Liu, Mild solution of second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces, Qual. Theory Dyn. Syst. 19 (2020), no. 1, Paper No. 5, 18 pp. https://doi.org/10.1007/s12346-020-00345-w
- N. Koo and H. Lee, Variationally stable implusive integro-differential systems, Dynam. Systems Appl. (to appear).
- G. K. Kulev and D. D. Bainov, Stability of the solutions of impulsive integro-differential equations in terms of two measures, RAIRO Model. Math. Anal. Numer. 25 (1991), no. 1, 93-110. https://doi.org/10.1051/m2an/1991250100931
- V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6, World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. https://doi.org/10.1142/0906
- V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and applications. Vol. I, Academic Press, New York, 1969.
- V. Lakshmikantham, X. Liu, and S. Sathananthan, Impulsive integro-differential equations and extension of Lyapunov's method, Appl. Anal. 32 (1989), no. 3-4, 203-214. https://doi.org/10.1080/00036818908839849
- V. Lakshmikantham and M. Rama Mohana Rao, Theory of Integro-Differential Equations, Stability and Control: Theory, Methods and Applications, 1, Gordon and Breach Science Publishers, Lausanne, 1995.
- X. Liu and K. Zhang, Impulsive systems on hybrid time domains, IFSR International Series in Systems Science and Systems Engineering, 33, Springer, Cham, 2019. https://doi.org/10.1007/978-3-030-06212-5
- M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), no. 1-2, 161-175. https://doi.org/10.1524/anly.1984.4.12.161
- M. Pinto, Stability of nonlinear differential systems, Appl. Anal. 43 (1992), no. 1-2, 1-20. https://doi.org/10.1080/00036819208840049
- M. Rama Mohana Rao, S. Sathananthan, and S. Sivasundaram, Asymptotic behavior of solutions of impulsive integrodifferential systems, Appl. Math. Comput. 34 (1989), no. 3, 195-211. https://doi.org/10.1016/0096-3003(89)90104-5
- M. Rama Mohana Rao, S. Sathananthan, and S. Sivasundaram, Stability of Volterra integro-differential equations with impulsive effect, J. Math. Anal. Appl. 163 (1992), no. 1, 47-59. https://doi.org/10.1016/0022-247X(92)90276-J
- A. M. Samoilenko and N. A. Perestyuk, Impulsive differential equations, translated from the Russian by Y. Chapovsky, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 14, World Scientific Publishing Co., Inc., River Edge, NJ, 1995. https://doi.org/10.1142/9789812798664
- P. S. Simeonov and D. D. Bainov, Stability of the solutions of a system of integrodifferential equations with impulse effect, Math. Rep. Toyama Univ. 9 (1986), 1-24.
- G. Tr. Stamov, Impulsive integro-differential equations and stability of moving invariant manifolds, Methods Appl. Anal. 14 (2007), no. 1, 69-76. https://doi.org/10.4310/MAA.2007.v14.n1.a6
- V. E. Tarasov, Fractional dynamics of relativistic particle, Internat. J. Theoret. Phys. 49 (2010), no. 2, 293-303. https://doi.org/10.1007/s10773-009-0202-z
- D. Xu, W. Zhu, and S. Long, Global exponential stability of impulsive integro-differential equation, Nonlinear Anal. 64 (2006), no. 12, 2805-2816. https://doi.org/10.1016/j.na.2005.09.020