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On exponential bounds for solutions of second order differential equations. (English) Zbl 0546.34029

The paper considers the solutions to the equation \(\ddot u+f(t)u=0\), \(t\geq 0\), where f is bounded and nonnegative, say \(0\leq f(t)\leq 1\). The main theorem of this paper proves that \(u(t)\) is \(O(e^{kt})\) where the best possible \(k\) is determined (approximately 0.244). The bound is attained for a function \(f\) which is periodic and piecewise constant with the values 0 and 1.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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