## 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

### Keywords:

generalized Hill’s equation; stability
Full Text: