AM  Vol.6 No.10 , September 2015
On Stability of Nonlinear Differential System via Cone-Perturbing Liapunov Function Method
ABSTRACT
Totally equistable, totally Φ0-equistable, practically equistable, and practically Φ0-equistable of system of differential equations are studied. Cone valued perturbing Liapunov functions method and comparison methods are used. Some results of these properties are given.

Cite this paper
Soliman, A. and Seyam, W. (2015) On Stability of Nonlinear Differential System via Cone-Perturbing Liapunov Function Method. Applied Mathematics, 6, 1769-1780. doi: 10.4236/am.2015.610157.
References
[1]   Lakshmikantham, V. and Leela, S. (1969) Differential and Integeral Inequalities. Vol. I, Academic Press, New York.

[2]   Lakshmikantham, V. and Leela, S. (1976) On Perturbing Liapunov Functions. Journal of Systems Theory, 10, 85-90.
http://dx.doi.org/10.1007/BF01683265

[3]   El Sheikh, M.M.A., Soliman, A.A. and Abd Alla, M.H. (2000) On Stability of Non Linear Systems of Ordinary Differential Equations. Applied Mathematics and Computation, 113, 175-198.
http://dx.doi.org/10.1016/S0096-3003(99)00082-X

[4]   Soliman, A.A. (2002) On Total Φ0-Stability of Non Linear Systems of Differential Equations. Applied Mathematics and Computation, 130, 29-38.
http://dx.doi.org/10.1016/S0096-3003(01)00087-X

[5]   Soliman, A.A. (2003) On Total Stability of Perturbed System of Differential Equations. Applied Mathematics Letters, 16, 1157-1162.
http://dx.doi.org/10.1016/S0893-9659(03)90110-8

[6]   Soliman, A.A. (2005) On Practical Stability of Perturbed Differential Systems. Applied Mathematics and Computation, 163, 1055-1060.
http://dx.doi.org/10.1016/j.amc.2004.06.073

[7]   Akpan, E.P. and Akinyele, O. (1992) On Φ0-Stability of Comparison Differential Systems. Journal of Mathematical Analysis and Applications, 164, 307-324.
http://dx.doi.org/10.1016/0022-247X(92)90116-U

[8]   Adeyeye, J.O. (2001) On Cone-Valued Lyapanov Functions and Stability in Two Measures for Integro-Differential Systems. Nonlinear Analysis, 47, 4835-4843.
http://dx.doi.org/10.1016/S0362-546X(01)00595-8

 
 
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