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Magdalena Nockowska-Rosiak

Publications and source records attributed to Magdalena Nockowska-Rosiak.

4 recordsLinked to original sources
arXiv2022

Positivity and discretization of Fredholm integral operators

We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding order cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained for the simplest ones based on polynomial, piecewise linear or specific cubic interpolation (collocation), as well as for piecewise constant basis functions in a Bubnov-Galerkin approach. However, for semi-discretizations using quadratic splines or $\sinc$-collocation we demonstrate that positivity is violated. Our results are illustrated in terms of eigenpairs for Krein-Rutman operators and form the basis of corresponding investigations for nonlinear integral operators.

math.DS↗
arXiv2016

Bounded solutions and asymptotic stability to nonlinear second-order neutral difference equations with quasi-differences

This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ Δ\left( r_{n} Δ\left( x_{n}+q_{n}x_{n-τ}\right)\right)= a_{n}f(x_{n-σ})+b_n%, \ n\geq n_0 $$ with respect to $(q_n)$. For $q_n\to1$, $q_n\in(0,1)$ the standard fixed point approach is not sufficed to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\ge 1$ and $\sup|q_n|<2^{1-p}$ using Krasnoselskii's fixed point theorem we obtain sufficient conditions of the existence of the solution which belongs to $l^p$ space.

math.CA↗