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Topological degree and stability of periodic solutions for certain differential equations. (English) Zbl 0677.34042

This paper analyzes the stability of periodic solutions of nonautonomous equations by means of degree theory. The main result is a characterization of asymptotically stable periodic solutions in terms of topological index, for a certain class of differential equations. This class was introduced by R. A. Smith [J. Math. Anal. Appl. 120, 679- 708 (1986; Zbl 0603.34033)] in order to extend Massera’s convergence theorem to some n-dimensional systems. These ideas are applied to the study of stable oscillations of a forced pendulum equation with friction.
Reviewer: R.Ortega

MSC:

34C25 Periodic solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
70B99 Kinematics

Citations:

Zbl 0603.34033
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