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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
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