The stability of the equilibrium of a conservative system
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.
scientific article; zbMATH DE number 930244