On a Fokker-Planck equation arising in population dynamics.
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are established.