In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： P...In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point 1 1/d, and there are two branches of the asymptotic eigenvalues： The first branch is accumulating towards 1 -2, and the other branch tends to -∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.展开更多
We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ...We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.展开更多
基金supported by Shanxi Youth Foundation under Grant No.2013021002-1the National Natural Science Foundation of China under Grant Nos.61074049 and 61273130
文摘In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point 1 1/d, and there are two branches of the asymptotic eigenvalues： The first branch is accumulating towards 1 -2, and the other branch tends to -∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.
文摘We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.
