Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems
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Authors
Junyan Bao
- College of Mathematics and Information Science, Hebei University, Baoding, 071002, China.
Xiaojing Liu
- College of Mathematics and Information Science, Hebei University, Baoding, 071002, China.
Peiguang Wang
- College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China.
Abstract
This paper introduces the notions of partially equi-integral stability and partially equi-integral
\(\phi_0\)-stability for two differential systems, and establishes some criteria on stability relative to the \(x\)-component by using the cone-valued Lyapunov functions and the comparison technique. An example
is also given to illustrate our main results.
Share and Cite
ISRP Style
Junyan Bao, Xiaojing Liu, Peiguang Wang, Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems, Journal of Mathematics and Computer Science, 16 (2016), no. 4, 472-480
AMA Style
Bao Junyan, Liu Xiaojing, Wang Peiguang, Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems. J Math Comput SCI-JM. (2016); 16(4):472-480
Chicago/Turabian Style
Bao, Junyan, Liu, Xiaojing, Wang, Peiguang. "Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems." Journal of Mathematics and Computer Science, 16, no. 4 (2016): 472-480
Keywords
- Differential systems
- partially integral stability
- partially integral \(\phi_0\)-stability
- cone-valued Lyapunov functions
- comparison technique.
MSC
References
-
[1]
E. P. Akpan, O. Akinyele , On the \(\phi_0\)-stability of comparison differential systems, J. Math. Anal. Appl., 164 (1992), 307-324.
-
[2]
M. M. A. El-Sheikh, A. A. Soliman, M. H. Abd Alla , On stability of nonlinear differential systems via cone-valued Liapunov function method, Appl. Math. Comput., 119 (2001), 265-281.
-
[3]
S. G. Hristova , Integral stability in terms of two measures for impulsive differential equations with ''supremum'' , Comm. Appl. Nonlinear Anal., 16 (2009), 37-49.
-
[4]
S. G. Hristova , Integral stability in terms of two measures for impulsive functional differential equations , Math. Comput. Modelling, 21 (2010), 100-108.
-
[5]
S. G. Hristova, I. K. Russinov, \(\phi_0\)-Integral stability in terms of two measures for differential equations, Math. Balkanica, 23 (2009), 133-144.
-
[6]
A. O. Ignatyve , On the Partial equiasymptotic stability in functional differential equations , J. Math. Anal. Appl., 268 (2002), 615-628.
-
[7]
V. Lakshmikantham, S. Leela , Differential and Integral Inequalities, Vol. I, Academic press, New York (1969)
-
[8]
A. A. Soliman , On stability for impulsive perturbed systems via cone-valued Lyapunov function method, Appl. Math. Comput., 157 (2004), 269-279.
-
[9]
A. A. Soliman, M. H. Abd Alla, Integral stability criteria of nonlinear differential systems, Math. Comput. Modelling, 48 (2008), 258-267.