Qualitative and quantitative theory of differential and difference equations with applications  Page description

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Details of project

  
Identifier
46929
Type K
Principal investigator Győri, István
Title in Hungarian Differenciál- és differenciaegyenletek kvalitatív és kvantitatív elmélete alkalmazásokkal
Title in English Qualitative and quantitative theory of differential and difference equations with applications
Panel Mathematics and Computing Science
Department or equivalent Department of Matematics (University of Pannonia)
Participants Hartung, Ferenc
Horváth Bokor, Rózsa
Horváth, László
Pituk, Mihály
Slezák, Bernát
Starting date 2004-01-01
Closing date 2007-12-31
Funding (in million HUF) 11.234
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Kutatásaink a következő témakörökhöz kapcsolódtak: Megoldások aszimptotikus jellemzése és stabilitása; integrálegyenletek és egyenlőtlenségek mértékterekben; differenciálegyenletek megoldásainak paraméterektől való differenciálható függése, paraméterek becslése; állapotfüggő késleltetésű differenciálegyenletek stabilitása. A 2004-2007 kutatási időszakban 31 publikációnk jelent meg. Dolgoztainkra az elmúlt négy évben 575, ezen belül a kutatási periódusban megjelent 31 publikációnkra pedig 57 hivatkozást regisztráltunk. Eredményeinkről 9 plenáris, 33 meghívott szekció és 16 szekció előadásban számoltunk be nemzetközi konferenciákon. Ezeken kívül 34 meghívott előadást tartottunk különböző hazai és külföldi egyetemek szakmai szemináriumain.
Results in English
Our research is related to the following topics: Asymptotic characterization and stability of solutions; integral equations and inequalities in measure spaces; differentiability of the solutions with respect to the parameters, and parameter estimation methods; stability of differential equations with state-dependent delays. 31 of our pubications have appeared in the research period 2004-2007. We have counted 575 citations of our papers in the last four years, including 57 citations of our 31 papers published in this period. We gave 9 plenary, 33 invited, and 16 contributed talks at international conferences, and 34 invited talks at research seminars of national and foreign universities.
Full text http://real.mtak.hu/1632/
Decision
Yes





 

List of publications

  
J.A.D. Appleby, I. Győri and D. Reynolds: Subexponential solutions of scalar linear integro-differential equations with delays, Functional Differential Equations, 11:1-2, 11-18., 2004
D. Greenhalgh and I. Győri: Existence and uniqueness of solutions of a perturbation of the Mckendrick-Von Foester equation, Functional Differential Equations, 11:1-2, 69-76, 2004
I. Győri and F. Hartung: Stability Results for Cellular Neural Networks with Delays, Proc. 7th Colloq. Qual. Theory Differ. Equ., Electr. J. Qual. Theor. Diff. Equ, 15, 1-9., 2004
R. Horváth-Bokor: On stability for numerical approximations of stochastic ordinary differential equations, Proc. 7th Colloq. Qual. Theory Differ. Equ., Electr. 1, Qual. Theor. Diff.Equ, 15, 1-9., 2004
U. Krause and M. Pituk: Boundedness and stability for higher order difference equations, J. Difference Equ. Appl., 10, 343-356., 2004
M. Pituk: A criterion for the exponential stability of linear difference equations, Appl. Math. Lett. 17, 779-783., 2004
M. Pituk: A note on the groth rates of nonoscillatory solutions of nonlinear difference equations, J. Difference Equ. Appl. 10, 1033-1036, 2004
I. Győri and M. Pituk: Asymptotically ordinary delay differential equations, Functional Differential Equations, 12, 187-208, 2005
M. Pituk: Cesaro summability in a linear autonomous difference equation, Proceedings of the American Mathematical Society, 133, 3333-3339., 2005
F. Hartung: Linearized stability in periodic functional differential equations with state-dependent delays, J. Computational and Applied Mathematics, 174:2, 201-211., 2005
F. Hartung and J. Turi: Identification of parameters in neutral functional differential equations with state-dependent delays, Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville, (Spain). 12-15 December 2005., 2005
T. Insperger, G. Stépán, F. Hartung, J. Turi: State dependent regenerative delay in milling processes, Proceedings of ASME International Design Engineering Technical Conferences, Long Beach CA, (2005), paper no. DETC2005-85282 (CD-ROM), 2005
E. Liz and M. Pituk: Asymptotic estimates and exponential stability for higher order monotone difference equations, Advances in Difference Equations, 2005:1, 41-55, 2005
L. Horváth: Generalizations of special Bihari type integral inequalities, Math. Inequal. Appl. 8, 440-449, 2005
J.A.D. Appleby, I. Győri and D. Reynolds: On exact convergence rates for solutions of linear systems of Volterra difference equations, J. Difference Equations and Applications, 12, 1257-1275, 2006
M. Pituk: A Perron type theorem for functional differential equations, Journal of Mathematical Analysis and Applications 316, 24-41, 2006
J.A.D. Appleby, I. Győri and D. Reynolds: On exact rates of solutions of linear systems of Volterra equations with delay, J. Math. Anal. Appl., 320, 56-77, 2006
I. Győri, F. Hartung: Fundamental solution and asymptotic stability of linear delay equations, Dyn. Contin. Discrete Impuls. Syst., 13:2, 261-288, 2006
F. Hartung, T. Insperger, G. Stépán, J. Turi: Approximate stability charts for milling processes under semi-discretization, Applied Mathematics and Computation, 174:1, 51-73, 2006
F. Hartung: On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays, J. Math. Anal. Appl., 324:1, 504-524, 2006
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, 435-545, 2006
L. Horváth: Nonlinear integral equations with increasing operators in measure spaces, Integral Equ. Appl., 17, 413-437, 2005
B. Slezák: On the noncontinuable solutions of retarded functional differential equations, Functional Differential Equations, 13:3-4, 603-635, 2006
E. Liz and M. Pituk: Exponential stability in a scalar functional differential equation, Journal of Inequalities and Applications, Volume 2006, Article ID 37195, pages 1-10, 2006
M. Pituk: Linearized oscillation in a nonautonomous scalar delay differential equation, Applied Mathematics Letters 19, 320-325, 2006
M. Pituk: Asymptotic behavior and oscillation of functional differential equations, Journal of Mathematical Analysis and Applications 322, 1140-1158, 2006
R. P. Agarwal and M. Pituk: Asymptotic expansions for higher-order scalar difference equations, Advances in Difference Equations, Volume 2007, Article ID 67492, 12 pages, 2007
J. A. D. Appleby, I. Győri, D. W. Reynolds: On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity, Note di Matematica, 27 (2007) 215-228., 2007
I. Győri, F. Hartung: Exponential Stability of a State-Dependent Delay System, Discrete and Continuous Dynamical Systems - Series A, 18:4 (2007) 773-791, 2007
M. Pituk: Asymptotic Behavior of Functional Differential Equations, MTA doktori értekezés, 2007
B. Slezák: On the parameter-dependence of the solutions of functional differential equations with unbounded state-dependent delay I. The upper-semicontinuity of the resolvent function, Int. J. Qualitative Theory of Differential Equations and Applications, 1:1 (2007), 88-114, 2007



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