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Convergence of Solutions of Third Order Differential Equations*

Published online by Cambridge University Press:  20 November 2018

K. E. Swick
K. E. Swick*
Affiliation:
Occidental College, Los Angeles, California
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Consider a system of differential equations . Solutions of this system are said to be convergent if, given any pair of solutions x(t), y(t), x(t) - y(t) → 0 as t → ∞. In this case the system is also said to be extremely stable.

In [6] a technique was developed which yielded the convergence of solutions of the forced Lienard equation. Here a similar technique i s applied to forced third order equations. A critical step in [6] was to show that a certain matrix was negative definite. This could be done directly in [6] since the matrix was only 2 × 2. With third and higher order equations, direct use of necessary and sufficient conditions is not feasible since the computations become unwieldy.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 779 - 792
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

This work was supported in part by National Science Foundation COSIP (GY 4754).

*

Much of this paper is a part of the author's Ph. D. dissertation at the University of Iowa. The author wishes to thank Professor P.E. Waltman for his advice and encouragement.

References

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