Spectral properties of general self-adjoint, even order differential operators
Spectral properties of fourth order differential operators
Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator , are established. These conditions are based on a recently proved relationship between spectral properties of and oscillation of a certain associated second order differential equation.
Rayleigh principle for linear Hamiltonian systems without controllability
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even order Sturm-Liouville differential equations.
Rayleigh principle for linear Hamiltonian systems without controllability
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Symmetric three-term recurrence equations and their symplectic structure.
Weyl-Titchmarsh theory for time scale symplectic systems on half line.
Terminal value problems for first and second order nonlinear equations on time scales.
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