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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...
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...
We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation
and we show that if (*) is regular, a solution of this equation such that for large is principal if and only if
Conditions on the functions are given which guarantee that (*) is regular.
Sufficient conditions for oscillation of a certain nonlinear trinomial third order differential equation are proved.
We consider the half-linear differential equation of the form
under the assumption that is integrable on . It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as .
We are concerned with the uniqueness problem for solutions to the second order ODE of the form , subject to appropriate initial conditions, under the sole assumption that is non-decreasing with respect to , for each fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable. The interest in this problem comes, among other, from the study of oscillations of lumped parameter systems with implicit...
This paper deals with the asymptotic behavior as of solutions to the forced Preisach oscillator equation , , where is a Preisach hysteresis operator, is a given function and is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function (or, in a more physical terminology, a balance condition between the hysteresis dissipation and the external forcing) which guarantees that every solution remains bounded for all times. Examples show...
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