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A necessary and sufficient condition for the asymptotic stability of the damped oscillator. (English) Zbl 0831.34052
The authors are interested in the solution of an old problem “to find the conditions on the damping coefficient \(h\) of the second order differential equation \(x'' + h(t)x' + k^2x = 0\) guaranteeing the asymptotic stability of the equilibrium \(x = x' = 0\).”
The authors prove by a very interesting method a new necessary and sufficient condition for the asymptotic stability and they deduce the relations between their results and the results of other authors.

MSC:
34D20 Stability of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
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