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The stability of the equilibrium of a conservative system. (English) Zbl 0873.34042

The generalized Hill’s equation \(x''+a(t) x^{2n+1}+e(t,x)=0\) is studied, where \(a\) is continuous and 1-periodic, \(e\) is also 1-periodic in \(t\) and dominated by the power \(x^{2n+2}\) in a neighbourhood of the origin. Sufficient conditions in terms of \(\int_0^1 a\) are given for the stability of the zero solution.
Reviewer: L.Hatvani (Szeged)

MSC:

34D20 Stability of solutions to ordinary differential equations
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