ICDDEA 2017‎ > ‎

e. Special Sessions

Dynamic equations on Time Scales

Martin Bohner
Missouri University of Science and Technology
e-mail: bohner@mst.edu

Rui A. C. Ferreira
University of Lisbon
e-mail: raferreira@fc.ul.pt

Time Scales Calculus, introduced in 1988 by the German mathematician Stefan Hilger, aimed in a first place to justify the words of Eric Temple Bell: A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.
Nevertheless, not only can this theory unify continuous and discrete analysis, as it is also able to extend the study of differential (continuous) and difference (discrete) equations to a more general class of dynamic equations, which includes, e.g., quantum-difference equations.
Nowadays it is a well established theory with many mathematicians researching within this topic. In this special session, we aim to bring together experts within the fields of differential, difference and dynamic equations, and provide a forum for fruitful discussions on the subject. Specifically, we invite researchers in any of the areas of fractional / ordinary / partial / delay / linear / nonlinear differential, difference, and dynamic equations and their applications.

Asymptotic problems for ODEs: qualitative theory and methods

Zuzana Dosla
Masaryk University
Czech Republic
e-mail: dosla@math.muni.cz

Mauro Marini 
University of Florence,
e-mail: mauro.marini@unifi.it

Recent trends in qualitative theory of ordinary differential equations. In particular asymptotic and oscillatory behavior of solutions, boundary value problems on the half-line, topological methods.

Nonautonomous dynamical systems

Martin Rasmussen
Imperial College of London
United Kingdom
 e-mail: m.rasmussen@imperial.ac.uk

Christian Pötzsche
Alpen-Adria Universität Klagenfurt
e-mail: christian.poetzsche@aau.at

Many dynamical systems modelling real-world problems are nonautonomous, i.e. they may involve parameters depending on time, controls or randomness. Prototypical examples of nonautonomous dynamical systems are periodically or almost periodically forced systems, but in principle the time-dependence can be arbitrary. Well-established methods and results for classical autonomous systems are no longer applicable in the context of nonautonomous dynamical systems and require appropriate extensions.
The theory of nonautonomous dynamical systems has experienced a renewed and steadily growing interest in the last thirty years. In this session, we cover recent developments in the theory of nonautonomous dynamical systems.

Concrete nonlinear difference equations and systems and asymptotic methods

Malgorzata Migda
Poznan University of Technology
e-mail: malgorzata.migda@put.poznan.pl

Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
e-mail: sstevic@ptt.rs

Recently there has been a considerable interest in studying of the long-term behavior of solutions to various types of concrete difference equations and systems. Numerous methods and ad hoc tricks have been used in the study. Asymptotic methods are some of them and they are used in these, as well as some classical equations and systems which are related to differential ones.

Oscillation of delay differential and difference equations

Istvan Gyori 
University of Pannonia
e-mail: gyori@almos.vein.hu

Mihaly Pituk
University of Pannonia
e-mail: pitukm@almos.uni-pannon.hu

The purpose of the special session is to present recent advances in the oscillation theory of delay differential and difference equations. Besides oscillation criteria, results on the large time behaviour of oscillatory and/or nonoscillatory solutions can also be presented. 

Recent trends on deterministic and stochastic partial differential equation

Tomás Caraballo
University of Sevilla
e-mail: caraball@us.es

Renato Colucci
University Niccolò Cusano
e-mail: renatocolucci@hotmail.com

Many issues in applied science can be formulated in terms of partial differential equations. However, our real world is non-deterministic by its own nature as noise and uncertainties are present everywhere. In this way, it can be more realistic in some cases to consider some kind of stochastic partial differential equations to describe the phenomenon. The main goals of this session will focus on the mathematical properties (well-posedness, existence and eventual uniqueness, regularity, stability, asymptotic behavior of solutions, ...) of both types of situations (deterministic and stochastic), and applications of these equations to real situations appearing in applied science.

Boundary Value Problems for Differential and Difference Equations

John R. Graef
University of Tennessee at Chattanooga
e-mail: john-graef@utc.edu

Feliz Minhós
University of Evora  ́
e-mail: fminhos@uevora.pt

This session is devoted to boundary value problems for differential and difference equations and their applications. The techniques used may be of a variational or topological nature.