## A Lyapunov-type stability criterion using $$L^\alpha$$ norms.(English)Zbl 1007.34053

The authors investigate the classical Lyapunov stability of Hill’s equation. A relation between the (anti-)periodic and the Dirichlet eigenvalues is used in order to establish some lower bounds for the first anti-periodic eigenvalue. The main result is a Lyapunov-type stability criterion using $$L^\alpha$$ norms. An example for illustration of the stability criterion is given.

### MSC:

 34D20 Stability of solutions to ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators 34C25 Periodic solutions to ordinary differential equations

### Keywords:

Hill’s equation; Lyapunov stability; eigenvalue
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### References:

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