Uniform global persistence of the nonlinear semiflow

Prove uniform global persistence for the nonlinear semiflow generated by the physiologically structured transport--renewal population model.

Background

The paper establishes only local threshold consequences for the reduced autonomous model at the extinction equilibrium: subcriticality implies local asymptotic stability, while supercriticality implies linear instability. It explicitly leaves unresolved the stronger global persistence question for the nonlinear semiflow, namely whether populations remain uniformly separated from extinction under appropriate supercritical conditions.

References

Other open problems include the proof of uniform global persistence for the nonlinear semiflow, the exact bifurcation structure at \mathcal R_0=1, and the derivation of first-order necessary optimality conditions via a rigorous backward adjoint system.

— Rigorous Analysis of a Nonlocal Transport--Renewal System for Physiologically Structured Populations  (2609.00735 - Yu et al., 1 Sep 2026) in Section Discussion