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Castelan, W. B.; Infante, E. F.

A Liapunov functional for a matrix neutral difference-differential equation with one delay. (English) Zbl 0415.34058

J. Math. Anal. Appl. 71, 105-130 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0415.34058

Cited in 14 Documents

MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
34K05 General theory of functional-differential equations

Keywords:

quadratic Liapunov functional; asymptotic stability; difference- differential equation; difference-differential equation with one delay
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References:

[1] Castelan, W. B.; Infante, E. F., On a functional equation arising in the stability theory of difference-differential equations, Quart. Appl. Math., 35, 311-319 (1977) · Zbl 0372.34043
[2] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602
[3] Hale, J. K., Functional Differential Equations, (Appl. Math. Science Series (1977), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0267.34064
[4] Hale, J. K., Ordinary Differential Equations (1967), Interscience: Interscience New York · Zbl 0189.39904
[5] Hale, J. K., Stability in linear systems of difference and differential-difference equations, (Proceedings of the Conference on Differential Equations (December 1976), Kyoto University: Kyoto University Kyoto), 10-70 · Zbl 0753.34048
[6] Hale, J. K., Sufficient conditions for stability and instability of autonomoux functional differential equations, J. Differential Equations, 1, 452-482 (1965) · Zbl 0135.30301
[7] D. Henry; D. Henry
[8] Infante, E. F.; Castelan, W. B., A Liapunov functional for a matrix differential-difference equation, (J. Differential Equations, 29 (1978)), 439-451 · Zbl 0354.34049
[9] E. F. Infante and J. A. WalkerProc. Roy. Soc. Edinburgh Sect. A; E. F. Infante and J. A. WalkerProc. Roy. Soc. Edinburgh Sect. A · Zbl 0417.34111
[10] Lancaster, P., Theory of Matrices (1969), Academic Press: Academic Press New York · Zbl 0186.05301
[11] J. P. LaSallein; J. P. LaSallein · Zbl 0159.12002
[12] J. P. LaSalle; J. P. LaSalle · Zbl 0606.93001
[13] Melvin, W. R., A class of neutral functional differential equations, J. Differential Equations, 12, 524-534 (1972) · Zbl 0234.34083
[14] Melvin, W. R., Stability properties of functional differential equations, J. Math. Anal. Appl., 48, 749-763 (1974) · Zbl 0311.39002
[15] M. Sendaula; M. Sendaula · Zbl 0352.49004
[16] Walker, J. A., On the application of Liapunov’s direct method to linear dynamical systems, J. Math. Anal. Appl., 53, 187-220 (1976) · Zbl 0338.34066
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