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### Open Access Journals

DCDS-B

Most mathematicians who in their professional career deal with differential
equations, PDEs, dynamical systems, stochastic equations and a variety of
their applications, particularly to biomedicine, have come across the research
contributions of Avner Friedman to these fields. However, not many of them
know that his family background is actually Polish. His father was born in the
small town of Włodawa on the border with Belarus and lived in another Polish
town, Łomza, before he emigrated to Israel in the early 1920's (when it
was still the British Mandate, Palestine). His mother came from the even
smaller Polish town Knyszyn near Białystok and left for Israel a few years
earlier. In May 2013, Avner finally had the opportunity to visit his father's
hometown for the first time accompanied by two Polish friends, co-editors of
this volume. His visit in Poland became an occasion to interact with Polish
mathematicians. Poland has a long tradition of research in various fields
related to differential equations and more recently there is a growing
interest in biomedical applications. Avner visited two research
centers, the Schauder Center in Torun and the Department of Mathematics of the
Technical University of Lodz where he gave a plenary talk at a one-day
conference on Dynamical Systems and Applications which was held on this
occasion. In spite of its short length, the conference attracted
mathematicians from the most prominent research centers in Poland including
the University of Warsaw, the Polish Academy of Sciences and others, and even
some mathematicians from other countries in Europe. Avner had a chance to get
familiar with the main results in dynamical systems and applications presented
by the participants and give his input in the scientific discussions. This
volume contains some of the papers related to this meeting and to the overall
research interactions it generated. The papers were written by mathematicians,
mostly Polish, who wanted to pay tribute to Avner Friedman on the occasion of
his visit to Poland.

For more information please click the “Full Text” above.

For more information please click the “Full Text” above.

keywords:

DCDS-B

A class of a higher-order nonlinear difference system with delayed arguments where the first equation of the system is of a neutral type is considered. A classification of non-oscillatory solutions is given and results on their boundedness or unboundedness are derived. The obtained results are illustrated by examples.

DCDS-B

A class of higher order nonlinear neutral difference equations with quasidifferences is studied. Sufficient conditions under which considered equation has a solution which converges to zero are presented.

DCDS-B

The 2-dimensional system of neutral type nonlinear difference equations with delays in the following form

$\left\{ \begin{align}&Δ≤(x_1(n)-p_1(n)\,x_1(n-τ_1))=a_1(n)\,f_1(x_1(n-σ_1),x_2(n-σ_2))\\&Δ≤(x_2(n)-p_2(n)\,x_2(n-τ_2))=a_2(n)\,f_2(x_1(n-σ_3),x_2(n-σ_4)),\end{align} \right.$ |

is considered. In this paper we use Schauder's fixed point theorem to study the existence of periodic solutions of the above system.

keywords:
System of difference equation
,
delays
,
2-dimensional
,
neutral type
,
periodic solutions
,
existence

DCDS-B

A Volterra difference equation of the form
$$x(n+2)=a(n)+b(n)x(n+1)+c(n)x(n)+\sum\limits^{n+1}_{i=1}K(n,i)x(i)$$
where $a, b, c, x \colon\mathbb{N} \to\mathbb{R}$ and $K \colon \mathbb{N}\times\mathbb{N}\to \mathbb{R}$ is studied. For every admissible constant $C \in \mathbb{R}$, sufficient conditions for the existence of a solution $x \colon\mathbb{N} \to\mathbb{R}$ of the above equation such that
\[
x(n)\sim C \, n \, \beta(n),
\]
where $\beta(n)= \frac{1}{2^n}\prod\limits_{j=1}^{n-1}b(j)$, are presented. As a corollary of the main result, sufficient conditions for the existence of an eventually positive, oscillatory, and quickly oscillatory solution $x$ of this equation are obtained. Finally, a conditions under which considered equation possesses an asymptotically periodic solution are given.

keywords:
periodic solutions.
,
nonoscillatory
,
linear equation
,
Volterra difference equation
,
oscillatory

DCDS-B

This work is devoted to the study of the existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with *p*-Laplacian.

## Year of publication

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