The existence of an equilibrium for permanent systems
The property of permanence in biological populations described by the ODE \(\dot x_ i=x_ i\cdot f_ i(^{\rightharpoonup})\), \(i=1,...,n\) (or by a corresponding difference equation) implies the existence of an equilibrium point in the interior of \({\mathbb{R}}^ n_+\). This known fact is proved in a simple way by application of Schauder's fixed point theorem. Analogous results are derived for a class of differential-delay equations by means of Horn's theorem.
scientific article; zbMATH DE number 4191455
scientific article