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Stability of finite difference schemes for generalized von Foerster equations with renewal

Leszczyński H., Zwierkowski P.

Opuscula Mathematica

2014

Vol. 34, no. 2

375--386

We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to l1 and l∞ norms.

Comparison ODE theorems related to the method of lines

Leszczyński H.

Journal of Applied Analysis

2011

Vol. 17, nr 1

137-154

We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.

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

Leszczyński H.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

219--223

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 con be obtained by classical (elementary) methods, instead of tarski's fixed point theorems in partially ordered spaces.