Qualitative Properties of Differential and Difference Equations  Page description

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Details of project

  
Identifier
101217
Type K
Principal investigator Győri, István
Title in Hungarian Differenciál- és differenciaegyenletek kvalitatív tulajdonságai
Title in English Qualitative Properties of Differential and Difference Equations
Keywords in Hungarian késleltetett ardumentumú differenciálegyenletek, differenciaegyenletek, stabilitás, lp-beli megoldások, egyenlőtlenségek, limesz formulák, aszimptotikus jellemzés, állapotfüggő késleltetés
Keywords in English delay differential equations, difference equations, stability, p-summability, inequalities, limit formulas, asymptotic representation, state-dependent delays
Discipline
Mathematics (Council of Physical Sciences)100 %
Ortelius classification: Differential equations
Panel Mathematics and Computing Science
Department or equivalent Department of Matematics (University of Pannonia)
Participants Hartung, Ferenc
Horváth, László
Pituk, Mihály
Starting date 2012-04-01
Closing date 2016-11-30
Funding (in million HUF) 16.046
FTE (full time equivalent) 8.44
state closed project
Summary in Hungarian
A pályázat keretében közönséges és késleltetett argumentumú differenciálegyenleteket, differenciaegyenleteket, integrálegyenleteket és integrál-egyenlőtlenségeket kívánunk vizsgálni. Vizsgálataink fő tárgya a nemlineáris és aszimptotikusan lineáris rendszerek megoldásainak kvalitatív tulajdonságai. A neutrális funkcionál-differenciálegyenletek illetve racionálisan független késleltetésű differenciaegyenletek esete rendkívül érdekesnek ígérkezik. Mivel a megoldások tanulmányozása során a Gronwall-típusú egyenlőtlenségek fontos szerepet játszanak, folytatni kívánjuk ez irányú kutatásainkat is. A fő hangsúlyt a nemlineáris differenciál- és differenciaegyenlőtlenségek vizsgálatára helyezzük. Kutatásaink másik fontos tárgya az állapotfüggő késleltetésű egyenletek megoldásainak kvalitatív vizsgálata. Ezen belül főként a paraméterek szerinti differenciálhatóságra fogunk szorítkozni. Tervezzük a korábbi differenciálhatósági eredményeink megjavítását.

A közös pályázatunk alapja a résztvevők között az elmúlt 18 év során kialakult sikeres együttműködés. Ez az együttműködés számos közös cikk születéséhez vezetett.
Summary
The subjects of our investigations are ordinary and delay differential equations, difference equations, integral equations and inequalities. We will study the qualitative properties of the solutions of nonlinear and asymptotically linear systems. The stability and asymptotic properties of the solutions are the most important subjects of our investigations. The case of neutral functional differential equations and difference equations with rationally independent delays seems to be most challenging. Since Gronwall-type inequalities play an important role in the study of the solutions, we will continue our research in this direction with an emphasis on nonlinear differential and difference inequalities. Another subject of our investigation is the study of the qualitative properties of the solutions of differential equations with state-dependent delays. We will focus on the differentiability with respect to the parameters. We have some ideas about possible improvements of previous differentiability results.

Our proposal is based on the successful cooperation between the applicants during the last 18 years. This cooperation led to numerous joint papers.




 

Final report

  
Results in Hungarian
Kutatásaink a differenciál- és differenciaegyenletek kvalitatív tulajdonságainak vizsgálatához, elsősorban stabilitási kérdésekhez, a megoldások aszimptotikus jellemzéséhez, az integrál- és diszkrét egyenlőtlenségek és az állapotfüggő késleltetésű egyenletek témaköréhez kapcsolódnak. A 2012-2016 kutatási időszakban 34 publikációnk jelent meg, melyek közül 1 monográfia, 25 impakt faktoros folyóiratcikk, az összesített impakt faktor 25,42. Dolgozatainkra az elmúlt 5 évben 938, ezen belül a kutatási periódusban megjelent 34 publikációnkra pedig eddig 29 hivatkozást regisztráltunk. Eredményeinkről 32 meghívott és további 16 előadásban számoltunk be nemzetközi konferenciákon. Ezeken kívül összesen 7 meghívott előadást tartottunk különböző hazai és külföldi egyetemek szakmai szemináriumain. A pályázati időszakban 4 alkalommal vettünk részt nemzetközi konferencia szervezésében.
Results in English
Our research is related to the qualitative properties of differential and difference equations, especially to the following topics: stability and asymptotic characterization of solutions; integral and discrete inequalities; differential equations with state-dependent delays. In the research period 2012-2016, we have published 34 research papers, including 1 monograph, and 25 have appeared in international journals with impact factor. The total impact factor of these papers is 25.42. We have counted 938 citations of our papers in the last 5 years, including 29 citations of the 34 papers published in the period of the project. We presented 32 invited lectures and 16 contributed talks at international conferences and we gave 7 invited talks in research seminars at national and foreign universities. In the research period we took part in the organization of 4 international conferences.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=101217
Decision
Yes





 

List of publications

  
Awwad E., Győri I., Hartung F.: BIBO stabilization of feedback control systems with time dependent delays, Applied Mathematics and Computation, v. 219, pp. 1485-1509, 2012
Győri I, Reynolds D: Explicit asymptotic limits for a class of discrete Volterra equations, Journal of Difference Equations and Applications, 18:11, pp. 1925-1930, 2012
Horváth L: A refinement of the integral form of Jensen's inequality, Journal of Inequalities and Applications, Paper 2012:178. 19 p., 2012
Horváth L., Khuram Ali Khan, J Pečarić: Further refinement of results about mixed symmetric means and Cauchy means, Advances in Inequalities and Applications, 1:1, pp. 12-32, 2012
Horvath L, Khuram Ali Khan, Josip Pecaric: On parameter dependent refinement of discrete Jensen's inequality for operator convex functions, Journal of Mathematical and Computational Science, 2:3, pp. 656-672, 2012
Pituk M: A limit boundary value problem for a nonlinear difference equation, Computers and Mathematics with Applications 64, pp. 2364-2369, 2012
Hartung F: Parameter estimation by quasilinearization in differential equations with state-dependent delays, Discrete and Continuous Dynamical Systems-B, 18:6, pp. 1611-1631, 2013
Hartung F., Turi J.: Identification in a Respiratory Control System Model, in Batzel J J, Bachar M, Kappel F (ed.) Mathematical Modeling and Validation in Physiology: Applications to the Cardiovascular and Respiratory Systems,Springer, 105-118, 2013
Hartung F.: On Differentiability of Solutions with respect to Parameters in Neutral Differential Equations with State-Dependent Delays, Annali di Matematica Pura ed Applicata, v. 192, pp. 17-47, 2013
Awwad E., Győri I., Hartung F.: BIBO stabilization of feedback control systems with time dependent delays, Applied Mathematics and Computation, v. 219, pp. 1485-1509, 2012
Pituk M.: Large time behavior of a linear difference equation with rationally non-related delays, Journal of Mathematical Analysis and Applications, v. 400(1), pp. 239-246, 2013
Pituk M: A limit boundary value problem for a nonlinear difference equation, Computers and Mathematics with Applications 64, pp. 2364-2369, 2012
Awwad E., Győri I., Hartung F.: BIBO stabilization of feedback control systems with time dependent delays, Applied Mathematics and Computation, v. 219, pp. 1485-1509, 2012
Győri I, Horváth L: Existence of periodic solutions in a linear higher order system of difference equations, Computers and Mathematics with Applications, 66:11, pp. 2239-2250, 2013
Győri I., Horváth L.: On Linear Difference Equations for which the Global Periodicity Implies the Existence of an Equilibrium, Abstract and Applied Analysis, 2013: Paper 971394, 2013
Horváth L.: A new refinement of the discrete Jensen's inequality depending on parameters, Journal of Inequalities and Applications, Paper 2013:551, 2013
Horváth L., Khuram Ali Khan, J. Pecaric: New refinements of Hölder and Minkowski inequalities with weights, Proceedings of A. Razmadze Mathematical Institute, 161, pp. 97-116, 2013
Hartung F.: On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays, Journal of Dynamics and Differential Equations, 25:4, pp. 1089-1138, 2013
Győri I., Horváth L.: Widely applicable periodicity results for higher order difference equations, Journal of Difference Equations and Applications, 20:(5-6) pp. 883-924, 2014
Győri I., Horváth L.: Utilization of the circulant matrix theory in periodic higher order autonomous difference equations, International Journal of Differential Equations and Applications, 9:(2) pp. 163-185, 2014
Horváth L., 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
Horváth L.: Weighted form of a recent refinement of the discrete Jensen's inequality, Mathematical Inequalities & Applications, 17:(3) pp. 947-961, 2014
Horváth L., Khuram Ali Khan, Josip Pečarić: Refinement of Jensen's inequality for operator convex functions, Advances in Inequalities and Applications, Article ID 26, pp. 1-17, 2014
Pituk M., Röst G.: Large time behavior of a linear delay differential equation with asymptotically small coefficient, Boundary Values Problems, 2014, Article ID: 114, 2014
Pituk M: A limit boundary value problem for a nonlinear difference equation, Computers and Mathematics with Applications 64, pp. 2364-2369, 2012
Győri I, Horváth L: Existence of periodic solutions in a linear higher order system of difference equations, Computers and Mathematics with Applications, 66:11, pp. 2239-2250, 2013
Győri I., Horváth L.: On Linear Difference Equations for which the Global Periodicity Implies the Existence of an Equilibrium, Abstract and Applied Analysis, 2013: Paper 971394, 2013
Hartung F: Parameter estimation by quasilinearization in differential equations with state-dependent delays, Discrete and Continuous Dynamical Systems-B, 18:6, pp. 1611-1631, 2013
Hartung F.: On Differentiability of Solutions with respect to Parameters in Neutral Differential Equations with State-Dependent Delays, Annali di Matematica Pura ed Applicata, v. 192, pp. 17-47, 2013
Hartung F.: On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays, Journal of Dynamics and Differential Equations, 25:4, pp. 1089-1138, 2013
Hartung F., Turi J.: Identification in a Respiratory Control System Model, in Batzel J J, Bachar M, Kappel F (ed.) Mathematical Modeling and Validation in Physiology: Applications to the Cardiovascular and Respiratory Systems,Springer, 105-118, 2013
Horváth L.: A new refinement of the discrete Jensen's inequality depending on parameters, Journal of Inequalities and Applications, Paper 2013:551, 2013
Horváth L., Khuram Ali Khan, J. Pecaric: New refinements of Hölder and Minkowski inequalities with weights, Proceedings of A. Razmadze Mathematical Institute, 161, pp. 97-116, 2013
Pituk M.: Large time behavior of a linear difference equation with rationally non-related delays, Journal of Mathematical Analysis and Applications, v. 400(1), pp. 239-246, 2013
Győri I., Horváth L.: Widely applicable periodicity results for higher order difference equations, Journal of Difference Equations and Applications, 20:(5-6) pp. 883-924, 2014
Győri I., Horváth L.: Utilization of the circulant matrix theory in periodic higher order autonomous difference equations, International Journal of Differential Equations and Applications, 9:(2) pp. 163-185, 2014
Horváth L.: Weighted form of a recent refinement of the discrete Jensen's inequality, Mathematical Inequalities & Applications, 17:(3) pp. 947-961, 2014
Horváth L., Khuram Ali Khan, Josip Pečarić: Refinement of Jensen's inequality for operator convex functions, Advances in Inequalities and Applications, Article ID 26, pp. 1-17, 2014
Pituk M., Röst G.: Large time behavior of a linear delay differential equation with asymptotically small coefficient, Boundary Values Problems, 2014, Article ID: 114, 2014
Čermák J, Gyori I, Nechvátal L: On explicit stability conditions for a linear fractional difference system, Fractional Calculus and Applied Analysis, 18:3, pp. 651-672, 2015
Chatzarakis G, I Győri, H Péics, I Stavroulakis: Existence of positive solutions of linear delay difference equations with continuous time, Electron J Qual Theor Differ Equat, 2015:15, pp. 1-23, 2015
Chieocan R, Pituk M: Weighted limits for Poincare difference equations, Applied Mathematics Letters, 49, pp. 51-57, 2015
Győri I, Hartung F, Mohamady N A: On a nonlinear delay population model, Applied Mathematics and Computations, 270, pp. 909-925, 2015
Horváth L: Infinite refinements of the discrete Jensen's inequality defined by recursion, Journal of Mathematical Inequalities, 9:4, pp. 1115-1132, 2015
Horváth L, Kh A Khan, J Pecaric: Refinements of determinental inequalities of Jensen's type, Eurasian Math J, 6:3, pp. 30-44, 2015
Horváth L, J. Pečarić: New versions of weighted multidimensional functional and Stolarsky means, Acta Mathematica Hungarica, 147:1, pp. 81-96, 2015
Horváth L, J Pečarić: Refinements of the classical Jensen's inequality coming from refinements of the discrete Jensen's inequality, Advances in Inequalities and Applications, 2015, Article ID: Art ID 8, pp. 1-17, 2015
Győri I., Hartung F., Mohamady N.: Existence and uniqueness of positive solutions of a system of nonlinear algebraic equations, Periodica Mathematica Hungarica, DOI 10.1007/s10998-016-0179-3, 2016
Győri I., Pituk M.: Asymptotic formulas for a scalar linear delay differential equation, Electron. J. Qual. Theory Differ. Equ., 2016:72, pp. 1-14, 2016
Hartung F: Differentiability of solutions with respect to the delay function in functional differential equations, Electron. J. Qual. Theory Differ. Equ., 2016:73, pp. 1-16, 2016
Hartung F: Nonlinear Variation of Constants Formula for Differential Equations with State-Dependent Delays, Journal of Dynamics and Differential Equations, 28:3, pp.1187-1213, 2016
Pituk, M.: The local spectral radius of a nonnegative orbit of compact linear operators, Mathematica Slovaca, 66:3, pp. 707-714, 2016



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