The Point Spectrum of the Linearized Boltzmann Operator with the External-force Term in a Bounded Domain

We will investigate the point spectrum on the imaginary axis of the linearized Boltzmann operator with an external-force potential in a bounded domain whose boundary is sufficiently smooth. The boundary condition considered is the perfectly reflective boundary condition. The point spectrum on the imaginary axis is only equal to {0}. However, the null space varies with the common axes of symmetry of the domain and the external-force potential.