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Lyapunov-Razumikhin method for differential equations with piecewise constant argument
| 1. | Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey, Turkey |
| [1] |
Lars Grüne, Peter E. Kloeden, Stefan Siegmund, Fabian R. Wirth. Lyapunov's second method for nonautonomous differential equations. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 375-403. doi: 10.3934/dcds.2007.18.375 |
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Fuke Wu, Xuerong Mao, Peter E. Kloeden. Discrete Razumikhin-type technique and stability of the Euler--Maruyama method to stochastic functional differential equations. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 885-903. doi: 10.3934/dcds.2013.33.885 |
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Marat Akhmet. Quasilinear retarded differential equations with functional dependence on piecewise constant argument. Communications on Pure and Applied Analysis, 2014, 13 (2) : 929-947. doi: 10.3934/cpaa.2014.13.929 |
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Zuowei Cai, Jianhua Huang, Lihong Huang. Generalized Lyapunov-Razumikhin method for retarded differential inclusions: Applications to discontinuous neural networks. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3591-3614. doi: 10.3934/dcdsb.2017181 |
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Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete and Continuous Dynamical Systems - B, 2015, 20 (8) : 2333-2360. doi: 10.3934/dcdsb.2015.20.2333 |
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F. M. G. Magpantay, A. R. Humphries. Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : 85-104. doi: 10.3934/dcdss.2020005 |
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Bi Ping, Maoan Han. Oscillation of second order difference equations with advanced argument. Conference Publications, 2003, 2003 (Special) : 108-112. doi: 10.3934/proc.2003.2003.108 |
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Omar Saber Qasim, Ahmed Entesar, Waleed Al-Hayani. Solving nonlinear differential equations using hybrid method between Lyapunov's artificial small parameter and continuous particle swarm optimization. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 633-644. doi: 10.3934/naco.2021001 |
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Fuke Wu, George Yin, Le Yi Wang. Razumikhin-type theorems on moment exponential stability of functional differential equations involving two-time-scale Markovian switching. Mathematical Control and Related Fields, 2015, 5 (3) : 697-719. doi: 10.3934/mcrf.2015.5.697 |
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Xiaofei He, X. H. Tang. Lyapunov-type inequalities for even order differential equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 465-473. doi: 10.3934/cpaa.2012.11.465 |
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W. Sarlet, G. E. Prince, M. Crampin. Generalized submersiveness of second-order ordinary differential equations. Journal of Geometric Mechanics, 2009, 1 (2) : 209-221. doi: 10.3934/jgm.2009.1.209 |
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Nobuyuki Kato, Norio Kikuchi. Campanato-type boundary estimates for Rothe's scheme to parabolic partial differential systems with constant coefficients. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 737-760. doi: 10.3934/dcds.2007.19.737 |
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Qiyuan Wei, Liwei Zhang. An accelerated differential equation system for generalized equations. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021195 |
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Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad, Saed F. Mallak, Hussam Alrabaiah. Lyapunov type inequality in the frame of generalized Caputo derivatives. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2335-2355. doi: 10.3934/dcdss.2020212 |
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Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203 |
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Ravi P. Agarwal, Abdullah Özbekler. Lyapunov type inequalities for $n$th order forced differential equations with mixed nonlinearities. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2281-2300. doi: 10.3934/cpaa.2016037 |
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Ezzeddine Zahrouni. On the Lyapunov functions for the solutions of the generalized Burgers equation. Communications on Pure and Applied Analysis, 2003, 2 (3) : 391-410. doi: 10.3934/cpaa.2003.2.391 |
| [18] |
Zoltan Satmari. Iterative Bernstein splines technique applied to fractional order differential equations. Mathematical Foundations of Computing, 2021 doi: 10.3934/mfc.2021039 |
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Kuo-Shou Chiu. Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 659-689. doi: 10.3934/dcdsb.2021060 |
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Felipe Linares, M. Scialom. On generalized Benjamin type equations. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 161-174. doi: 10.3934/dcds.2005.12.161 |
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