Research Laboratory for Differential Equations and their Applications

Members of the research laboratory

Ferenc Hartung, DSc, professor, co-head
Mihály Pituk, DSc, professor, co-head
László Horváth, PhD, associate professor

Earlier members of the research laboratory

István Győri, DSc, professor emeritus, founding head of laboratory
David Reynolds, Senior Lecturer, School of Mathematical Sciences, Dublin City University
Bernát Slezák, PhD, associate professor
Essam Awwad, PhD student
Attila Benkő, PhD student
Beáta Krasznai, assistant professor

Activity of the research laboratory

Many biological, physical, chemical, engineering and economic processes can be modeled with equations where the actual change of the system also depends on its previous state. Delayed differential and difference equations can be used to model these processes. It is important for applications to obtain as much information as possible about the properties of the solutions of the models. The aim of our research is to develop new theoretical and numerical methods and apply them to practical problems, with which we can obtain new scientific results on the asymptotic behavior, stability, oscillation and differentiability of solutions of delayed differential and difference equations. Related to this, research is also being conducted in connection with the investigation of integral equations, impulsive equations, and integral and differential inequalities. Our results are mainly motivated by mathematical equations describing biological processes, neural networks and by models of mechanical motions.

Research results

Our research is related to the investigation of the qualitative properties of differential and difference equations, primarily to questions of stability, boundedness, positivity, asymptotic characterization of solutions, continuous and discrete integral inequalities and equations with state-dependent delays. Among the achieved results, we highlight a result related to the exact oscillation bound of a linear delayed differential equation, which has been an open question in the literature for 30 years In the research period 2019-2029, we have published 34 research papers, including 1 monograph, and 32 have appeared in international journals with impact factor. The total impact factor of these papers is 62,07. We have counted 827 citations of our papers in the last 5 years.

Most important publications

J. A. D. Appleby, I. Győri, D. W. Reynolds, On exact convergence rates for solutions of linear systems of Volterra difference equations, J. Difference Equations and Applications, 12 (2006) 1257- 1275.
O. Arino and M. Pituk: More on linear differential systems with small delays, Journal of Differential Equations 170 (2001), 381-407.
H. Bereketoglu, I. Győri., Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infininte delay, J. Math. Anal. Appl. 210 (1997) 279-291.
S.I. Butt, Horváth L., Pecaric D, Pecaric J: Cyclic Improvements of Jensen’s Inequalities - Cyclic Inequalities in Information Theory, (Monographs in Inequalities 18), Element, Zagreb, ISBN 978-953-197-686-2, 2020
Á. Garab, M. Pituk, C. Pötzsche: Linearized stability in the context of an example by Rodrigues and Solà-Morales, Journal of Differential Equations 269 (2020), 9838-9845.
I. Győri, Connections between compartmental systems with pipes and integro-differential equations, Mathematical Modelling 7 (1986), 1215-1238.
I. Győri, F. Hartung, Asymptotically exponential solutions in nonlinear integral and differential equations, J. Differential Equations, 249:6 (2010) 1322-1352.
Győri I, Hartung F, Mohamady N A, Permanence in a class of delay differential equations with mixed monotonicity, Electronic Journal of Qualitative Theory of Differential Equations 1417-3875, 2018:(53) , pp. 1-21, (2018)
I. Győri, L. Horváth, A new view of the l^p theory for a sytem of higher order difference equations, Computers and Mathematics with Applications, 59 (2010) 2918-2932.
I. Győri, L. Horváth: Explicit estimates and limit formulae for the solutions of linear delay functional differential systems with nonnegative Volterra type operators, Appl. Math. Comput., 385, 125451, (2020)
I. Győri, G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Science Publications, Clarendon Press. Oxford, 1991.
I. Győri,, I. S. Trofimchuk, Global attractivity and persistence in a discrete population model, J. Difference Equations and Applications, 6 (2000), 647-665.
F Hartung, Linearized stability in periodic functional differential equations with state-dependent delays, J. Computational and Applied Mathematics 174: (2) pp. 201-211.
F. Hartung, On second-order differentiability with respect to parameters for differential equations with state-dependent delays, J. Dynamics and Differential Equations 25: (4) (2013) 1089-1138.
F. Hartung: On numerical approximation of a delay differential equation with impulsive self-support condition, Applied Mathematics and Computation 418 Paper: 126818 (2022)
F. Hartung, T. Krisztin, H.-O. Walther, and J. Wu, Functional differential equations with state-dependent delay: theory and applications, in Handbook of Differential Equations: Ordinary Differential Equations, volume 3, edited by A. Canada, P. Drábek and A. Fonda, Elsevier, North-Holand, 2006, 435-545.
L. Horváth, Khuram Ali Khan, Josip Pečarić: Combinatorial Improvements of Jensen's Inequality: Classical and New Refinements of Jensen’s Inequality with Applications, Element d. o. o., 240 p. (Monographs in Inequalities, 8), ISBN: 978-953-197-594-0, 2014
G. Lipták, K.M. Hangos, M. Pituk, G. Szederkényi: Semistability of complex balanced kinetic systems with arbitrary time delays, Systems & Control Letters 114 (2018), 38-43.
M. Pituk: Convergence to equilibria in scalar nonquasimonotone functional differential equations, Journal of Differential Equations 193 (2003), 95-130.
M. Pituk: A Perron type theorem for functional differential equations, Journal of Mathematical Analysis and Applications 316 (2006), 24-41.
M. Pituk: Global asymptotic stability of nonautonomous master equations: A proof of the Earnshaw–Keener conjecture, Journal of Differential Equations 364 (2023), 456-470.
M. Pituk, I.P. Stavroulakis, J.I. Stavroulakis: Explicit values of the oscillation bounds for linear delay differential equations with monotone argument, Communications in Contemporary Mathematics 25 (03) (2023), 2150087.

Publications of the research laboratory (2000-2023)

Introduction of the founding head of laboratory

István Győri (1943-2022, MSc, University of Szeged, Hungary, 1968; CSc, Hungarian Academy of Sciences, Budapest, 1976; DSc Hungarian Academy of Sciences, Budapest, 1992) worked at A. Szent-Györgyi Medical University, Szeged from 1968 to 1993, where he was the founder and head of Computer Center (1970-1993). He was a Visiting Professor at University of Rhode Island (Providence, USA) from 1987 to 1989. He is a professor and head of Department of Mathematics and Computing, University of Pannonia (formerly University of Veszprém) from 1993 to 2013, and a professor emeritus from 2013. He served as a rector of University of Veszprém 1995-98. He received Grünwald Géza Award, János Bolyai Mathematical Society, Hungary, 1978; Neumann János Award, János Neumann Society of Computer Science, Hungary, 1992; “Prof. Hermann Niemmeyer Fernandez” honorary professorship at University of Santiago, Chile, 1994; Széchenyi Research Scholarship, Ministry of Education, Hungary 1997-2000; Bolyai Farkas scientific award from “Arany János Foundation for the Science” (foundation of the Hungarian Academic of Sciences), 2000;Albert Szent-Györgyi Research Award, Ministry of Education, Hungary, 2000; Order of Merit of the Hungarian Republic, Knight's Cross, 2009, Prima Prize, Veszprém County, in science category (2010), Eötvös József-wreath award of the Hungarian Academy of Sciences (2018). He is a founding member of Information Science & Technology PhD School, University of Pannonia; Editor-in-chief of „International Journal of Qualitative Theory of Differential Equations and Applications” (India) (2007-2016); Member of the editorial board of „Functional Differential Equations” (Izrael); „Advances in Difference Equatons” (USA); „Journal of Advanced Research in Dynamical and Control Systems” (USA); „Communications in Differential and Difference Equations” (India); „International Journal of Difference Equations and Dynamical Systems” (India); „International Journal of Dynamical Systems and Differential Equations” (India); „Far East Journal of Mathematics” (India); „Pacific-Asian Journal of Mathematics and Mathematical Sciences” (USA); „Mathematical Notes” (Miskolc, Hungary); „Alkalmazott Matematikai Lapok” (Hungary). István Győri has published 231 papers including 1 monograph and 151 journal papers, and he has more than 3700 independent references for his work.