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CONVERGENCE OF SOLUTIONS OF TIME-VARYING LINEAR SYSTEMS WITH INTEGRABLE FORCING TERM

  • JITSURO SUGIE (a1)
Abstract
Abstract

The following system is considered in this paper: The primary goal is to establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) and a forcing term p(t) for all solutions to converge to the origin (0,0) as . Here, the zero solution of the corresponding homogeneous linear system is assumed to be neither uniformly stable nor uniformly attractive. Sufficient conditions are given for asymptotic stability of the zero solution of the nonlinear perturbed system under the assumption that q(t,0,0)=0.

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References
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[2] A. Halanay , Differential Equations: Stability, Oscillations, Time Lags (Academic Press, New York, 1966).

[5] L. Hatvani , ‘On the uniform attractivity of solutions of ordinary differential equations by two Lyapunov functions’, Proc. Japan Acad. 67 (1991), 162167.

[6] L. Hatvani , ‘On the asymptotic stability for a two-dimensional linear nonautonomous differential system’, Nonlinear Anal. 25 (1995), 9911002.

[8] D. R. Merkin , Introduction to the Theory of Stability, Texts in Applied Mathematics, 24 (Springer, New York, 1997).

[9] N. Rouche , P. Habets and M. Laloy , Stability Theory by Liapunov’s Direct Method, Applied Mathematical Sciences, 22 (Springer, New York, 1977).

[10] A. Strauss and J. A. Yorke , ‘Perturbing uniformly stable linear systems with and without attraction’, SIAM J. Appl. Math. 17 (1969), 725738.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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