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A note on a Herzog’s and Lemmert’s paper

100%

Leszczyński H.

Commentationes Mathematicae

2005

tom 45

nr 2

We give an alternative view of the results published in the Herzog’s and Lemmert’s paper "On maximal and minimal solutions for \(x'(t) = F(t, x(t), x(h(t)))\), \(x(0) = x_0\)", Comment. Math. XL (2000), 93-102. One can observe that these results can be obtained by classical (elementary) methods, instead of Tarski’s fixed point theorems in partially ordered spaces.

Existence of solutions to generalized von Foerster equations with functional dependence

63%

Leszczyński H. , Zwierkowski P.

nr 3

201-210

We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).