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Stability criteria in terms of two measures for functional differential equations. (English) Zbl 1075.34076

Summary: Results involving uniform stability and uniform asymptotic stability in terms of two measures of delay differential equations by using Lyapunov functional techniques are established.

MSC:

34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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[1] Movchan, A.A., Stability of processes with respect to two metrics, Prikl. mat. mekh., 24, 988-1001, (1960)
[2] Lakshmikantham, V.; Leela, S.; Martynyuk, A.A., Stability analysis of nonlinear systems, (1989), Marcel Dekker New York · Zbl 0676.34003
[3] Lakshmikantham, V.; Leela, S.; Sivasundaram, S., Lyapunov functions on product spaces and stability theory of delay differential equations, J. math. anal. appl., 154, 391-402, (1991) · Zbl 0781.34050
[4] Lakshmikantham, V., Uniform asymptotic stability criteria for functional differential equations in terms of two measures, Nonlinear anal., 34, 1-6, (1998) · Zbl 0934.34064
[5] Bená, M.A.; de Godoy, S.M.S., On the stability in terms of two measures of perturbed neutral functional differential equations, Nonlinear anal., 47, 7, 4567-4578, (2001) · Zbl 1042.34583
[6] Dos Reis, J.G.; Bená, M.A., A stability theorem in terms of two measures, Nonlinear anal., 29, 7, 737-740, (1997) · Zbl 0952.34059
[7] Fu, X.; Liu, X., Uniform boundedness and stability criteria in terms of two measures for impulsive integro-differential equations, Appl. math. comput., 102, 237-255, (1999) · Zbl 0929.45005
[8] Fu, X.; Zhang, L., Criteria on boundedness in terms of two measures for Volterra type discrete systems, Nonlinear anal., 30, 5, 2673-2681, (1997) · Zbl 0889.39002
[9] Liu, X., Uniform asymptotic stability of abstract functional differential equations, J. math. anal. appl., 216, 626-643, (1997) · Zbl 0891.34073
[10] Zappalà, G., On total functional stability with two measures, Mathematiche, LIII, fasc. II, 263-275, (1998) · Zbl 1156.34328
[11] Fan, M.; Dishen, J.B.; Wan, Q.; Wang, K., Stability and boundedness of solutions of neutral functional differential equations with finite delay, J. math. anal. appl., 276, 545-560, (2002) · Zbl 1020.34067
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