Published online by Cambridge University Press: 20 November 2018
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.
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.
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