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.


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
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