Nonnegative Eigenfunction Research Articles

Eigenvalue Spectrum of the Neutron Transport Operator for a Fast Multiplying System

The eigenvalue spectrum of the neutron transport operator for fast multiplying systems is discussed under the continuous energy treatment and with the assumption of isotropic distribution of the neutrons emitted by scattering and fission. In particular, the sufficient conditions are presented for the existence and non-existence of what is known as the fundamental mode. Further, it will be shown that, if the energy transfer kernel is positive almost everywhere, then the eigenvalue for the fundamental mode is strictly larger than the real part of any other eigenvalue and there are no non-negative eigenfunctions excepting the fundamental mode.

Spectrum of an elliptic equation

It is shown that the spectrum for the first boundary-value problem for a second-order elliptic equation always lies in the half-plane λ0 ≤Re z, where is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. Apart from λ0, there are no other points of the spectrum on the straight line Re z=λ0.

Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator

Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator