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Lyapunov inequalities and stability for linear Hamiltonian systems. (English) Zbl 1242.37039

The paper considers qualitative properties of the Hamiltonian system

Ju ' =H(t)u,u= col (x T y T ) n

expressed via various Lyapunov-like inequalities. Discussed are the standard boundary value problem

x(a)=x(b)=0

and its applications to quantum mechanics. The paper ends with some stability criteria for planar Hamiltonian systems. All results can be seen as either improvements or generalizations of Lyapunov inequalities.

MSC:
37J25Stability problems (finite-dimensional Hamiltonian etc. systems)
34B05Linear boundary value problems for ODE
34D20Stability of ODE
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
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