Double Lipschitz Stability for Nonlinearly neutral Differential Systems with Multiple Delay


Double Lipschitz Stability for Nonlinearly neutral Differential Systems with Multiple Delay


Huo Ran1, Wang Xiaoli2*

1College of Science Inner Mongolia Agricultural University, Huhhot, 010018,China.
2College of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Huhhot, 010070, China.


Research Journal of Mathematics and Computer Science

In this paper, first we proves a class of time-delay differential inequalities. And then, the nonlinear differential systems with time delay are considered and it is obtained that the trivial solution of the nonlinear systems with time delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variable.


Keywords: Nonlinear systems; Partial variable stability; Lipschitz asymptotic stability; Differential inequality

Free Full-text PDF


How to cite this article:
Huo Ran, Wang Xiaoli. Double Lipschitz Stability for Nonlinearly neutral Differential Systems with Multiple Delay. Research Journal of Mathematics and Computer Science, 2020; 4:19. DOI: 10.28933/rjmcs-2020-03-1005


References:

1. Vorotnikov.V.I., On the theory of Lyapunov stability in critical cases, Dokl. Akad. Nank.367 (4) (1999) 481–484.
2. Vorotnikov.V.I., On problems of stablity with respect to some of the variables, Prikl.Mat.Meth. 63(5) (1999) 736–745.
3. Dannan. F.M., Elaydi.S., Lipschitz stablity of nonlinear differential equation, J. Math. Anan. Appl. 116 (1986) 562–579.
4. YU-LI Fu, On Lipschitz Stability For F. D. E., Pacific Journal of Mathematics. 151(2) (1991) 229–235.
5. SUNG KYU CHOI, KI SHIK KOO AND KEONHEE LEE, LIPSCHITZ STABILITY AND EXPONENTIAL ASYMPTOTIC STABILITY IN PERTURBED SYSTEMS, J. Korean Math. Soc. 29(1)(1992) 175–190.
6. Cordunmeanu C, Some problems concerning partial stablity, Symp.Math. 6(1971) 141–154.
7. Zhang Yi, K-Stablity of nonlinear systerm with time-delay, Scientia Sinica Mathematica. 37(3) (1994) 247–255.
8. Huo Ran, Wang Xiaoli, and Si Ligeng, Exponential asymptotic stablity for nonlinear neutral systems with multiple delay, Journal of Xu Zhou Normal University (Natural Science Edition)}. 26(2)} (2008) 80–84.
9. Huo Ran, Zhang Caiqin, Wang Xiaoli, and Si Ligeng, The Lipschitz stablity of a kind of nonlinear delay neutral differential systems based on a new integral inequality, Math.in Practice and Theory. 39(9) (2009) 231–234.
10. Dannan.F.M., Elaydi.S., Lipschitz stablity of nonlinear differential equation, J. Math. Anan. Anan.Appl. 116 (1986) 562–579.
11. Si Ligeng,Differential inequality and differential equation with time- delay, Inner Mongolia People’s Press. (2001).
12. Si Ligeng, The boundness and stability of solutions for nonlinear neutral differential systems with variable delay, Acta. Math. Sinica. (1974) 197–204.
13. Ran Huo, Xiaoli Wang. Double Lipschitz Stability for Non linearly Perturbed Differential Systems with Multiple Delay[J] Journal of Applied Mathematics and Physics, 2019, 7, 3003-3011.
14. Ran Huo, Xiaoli Wang.The Stabilities for a Class of Nonlinear Differential Systems with Time-Delay [J] Advances in Applied Mathematics, 2019, 8(11), 1845-1851