Total stability for neutral functional differential equations

Izé, A. F.; Freiria, A. A.

doi:10.1090/S0002-9939-1981-0597658-1

Total stability for neutral functional differential equations
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by A. F. Izé and A. A. Freiria

Proc. Amer. Math. Soc. 81 (1981), 437-442

DOI: https://doi.org/10.1090/S0002-9939-1981-0597658-1

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Abstract:

The basic idea of this work is to use Lyapunov functionals to show that for neutral functional differential equations, uniform asymptotic stability implies total stability.

References

Marianito Cruz A. and Jack K. Hale, Stability of functional differential equations of neutral type, J. Differential Equations 7 (1970), 334–355. MR 257516, DOI 10.1016/0022-0396(70)90114-2
Jack K. Hale, Functional differential equations, Applied Mathematical Sciences, Vol. 3, Springer-Verlag New York, New York-Heidelberg, 1971. MR 0466837
A. F. Izé and J. G. dos Reis, Stability of perturbed neutral functional differential equations, Nonlinear Anal. 2 (1978), no. 5, 563–571. MR 512152, DOI 10.1016/0362-546X(78)90004-4
Junji Kato and Yasutaka Sibuya, Catastrophic deformation of a flow and non-existence of almost periodic solutions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 2, 267–279. MR 466760
Orlando Lopes, Stability and forced oscillations, J. Math. Anal. Appl. 55 (1976), no. 3, 686–698. MR 446657, DOI 10.1016/0022-247X(76)90075-5
Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, vol. 9, Mathematical Society of Japan, Tokyo, 1966. MR 0208086