Corrections to "Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas" (Dissertationes Math. 291 (1990))
A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...
For a certain class of functional differential equations with perturbations conditions are given such that there exist solutions which converge to solutions of the equations without perturbation.
Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.