Delay makes problems in population modelling. (English) Zbl 0611.92023

Smítalová, K.

Differential equations and their applications, Equadiff 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 421-424 (1986).

[For the entire collection see Zbl 0595.00009.]
This short paper presents a few results which show some peculiarities of delay differential equations regarding general existence theory. Notably, generically, in the set of equations: \[ x'(t)=f(x(t-1)),\quad t>0;\quad x(t)=\phi (t),\quad -1\leq t\leq 0, \] the solution operator \(\phi\to x(.)\) is not injective.
The question of pointwise completeness is discussed, too. These properties are briefly commented upon in relation to the use of delay differential equations in population dynamics.

Reviewer: O.Arino

MSC:

92D25	Population dynamics (general)
34K05	General theory of functional-differential equations

Keywords:

delay differential equations; general existence theory; pointwise completeness; population dynamics

Citations:

Zbl 0595.00009