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Project detail
Duration: 01.01.2004 — 31.12.2006
Funding resources
Technologická agentura ČR - 1. veřejná soutěž Program podpory aplikovaného výzkumu, experimentálního vývoje a inovací DELTA 2 2019
- whole funder (2004-01-01 - 2006-12-31)
On the project
Projekt je zaměřen na studium limitních vlastností obyčejných a funkcionálních diferenciálních rovnic a navazuje na studium blízké problematiky v minulých letech, zejména při řešení grantu GA ČR 201/99/0295. Hlavním cílem je studium asymptotických a oscilačních vlastností řešení obyčejných diferenciálních rovnic 2. řádu s p-Laplacianem, singulárních řešení nelineárních diferenciálních rovnic vyšších řádů a studium transformací Hamiltonovských systémů a lineárních diferenciálních rovnic vyšších řádů. Dalším cílem je studium asymptotických vlastností funkcionálních diferenciálních rovnic s odkloněným argumentem a studium otázek stability. Hlavní výsledky budou publikovány v předních světových časopisech.
Description in EnglishThe project is focused on the investigation of limit properties of ordinary and functional differential equations. It is linked with similar problems investigated las years, mainly when the grant of the Grant Agency of the Czech Republic no. 201/99/0295 was solved. The following topics are the main goal of the project:asymptotic and oscillatory properties of solutions of ordinary second order differential equations with p-Laplacian, singular solutions of nonlinear higher order diffential equations. Further effort is devoted to the study of asymptotic properties of functional differential equations with deviating arguments and to stability problems. The acheived results will be published in the international mathematical journals.
Keywordsasymptotické vlastnosti, obyčejné diferenciální rovnice, funkcionální diferenciální rovnice
Key words in Englishasymptotic properties; ordinary differential equations; functional differential equations
Mark
IAA1163401
Default language
Czech
People responsible
Čermák Jan, prof. RNDr., CSc. - fellow researcherDošlá Zuzana, prof. RNDr., DSc. - principal person responsible
Units
Institute of Mathematics- co-beneficiary (2004-01-01 - 2006-12-31)
Results
DIBLÍK, J.; SVOBODA, Z. Remark on positive solutions of retarded functional differential equations. In 4. konference o matematice a fyzice na vysokých školách technických s mezinárodní účastí. Brno: Universita obrany Brno, 2005. p. 55 ( p.)ISBN: 80-85960-91-5.Detail
ČERMÁK, J. On the differential equation with power coefficients and proportional delays. Tatra Mountains Mathematical Publications, 2008, roč. 2007, č. 38, s. 57-69. ISSN: 1210-3195.Detail
ČERMÁK, J. Asymptotic properties of differential systems with unbounded delays. In 2004 - Dynamical systems and applications. Delhi (India): GBS Publishers & Distributors (India), 2005. p. 195 ( p.)ISBN: 81-89476-00-9.Detail
DIBLÍK, J.; SVOBODA, Z. Using the Wazewski's Topological Method for Functional Differential Equations with Unbounded Delay. In 5. Matematický workshop. Brno: FAST VUT, 2006. p. 39 ( p.)ISBN: 80-214-3282-9.Detail
DIBLÍK, J.; KÚDELČÍKOVÁ, M. Inequalities for the positive solutions of the equation $\dot y(t)=-\sum_{i=1}^n(a_i+b_i/t)y(t-\tau_i)$. In Proceedings of the Conference on Differential and Difference Equations and Applications, edited by Ravi. P. Agarwal and Kanishka Perera, Hindawi Publishing corporation, 2006. USA: Hindawi Publishing Corporation, 2007. p. 341-350. ISBN: 977-5945-38-0.Detail
KUNDRÁT, P. Asymptotic properties of the discretized pantograph equation. Studia Universitatis Babes-Bolyai Mathematica, 2005, vol. L, no. 1, p. 77 ( p.)ISSN: 0252-1938.Detail
DIBLÍK, J.; KOKSCH, N. Sufficient conditions for the existence of global solutions of delayed differential equations. Journal of Mathematical Analysis and Application, 2006, vol. 318 (2006), no. 1, p. 611 ( p.)ISSN: 0022-247X.Detail
ČERMÁK, J.; URBÁNEK, M. The asymptotic properties of the dynamic equation with a delayed argument. Opuscula Mathematica, 2006, vol. 26, no. 3, p. 421-429. ISSN: 1232-9274.Detail
ČERMÁK, J. On matrix differential equations with several unbounded delays. European Journal of Applied Mathematics, 2006, vol. 17, no. 7, p. 417-433. ISSN: 0956-7925.Detail
ČERMÁK, J.; URBÁNEK, M. On the asymptotics of solutions of delay dynamic equations on time scales. MATHEMATICAL AND COMPUTER MODELLING, 2007, vol. 46, no. 3-4, p. 445-458. ISSN: 0895-7177.Detail
ČERMÁK, J. The asymptotic behaviour of q -difference equations with multiple delays. Tatra Mountains Mathematical Publications, 2009, vol. 2009, no. 43, p. 41-50. ISSN: 1210-3195.Detail
DIBLÍK, J.; BAŠTINEC, J. Multipoint singular boundary-value problem for system of semilinear differential equations. Communications in Applied Analysis, 2007, vol. 10(2006), no. 4, p. 413-430. ISSN: 1083-2564.Detail
ČERMÁK, J. On a linear differential equation with a proportional delay. Mathematische Nachrichten, 2007, vol. 280, no. 5-6, p. 495-504. ISSN: 0025-584X.Detail
NEUMAN, F. Constructing and solving equations - inverse operations. AEQUATIONES MATHEMATICAE, 2005, vol. 2005, no. 70, p. 77 ( p.)ISSN: 0001-9054.Detail
DIBLÍK, J.; SVOBODA, Z. Positive solutions of p-type retarded functional differential equations. Nonlinear Analysis, Theory, Methods and Applications, 2006, vol. 64 (2006), no. 1, p. 1831-1848. ISSN: 0362-546X.Detail
DIBLÍK, J.; NOWAK, C. A nonuniqueness criterion for a singular system of two ordinary differential equations. Nonlinear Analysis, Theory, Methods and Applications, 2006, vol. 64 (2006), no. 1, p. 637-656. ISSN: 0362-546X.Detail
NEUMAN, F. On representation of a smooth system by discrete one. In Proceedings of the 10-th International Modelling School of AMSE-UAPL. Lviv, Ukraine: University of Technology, Lviv, 2005. p. 149 ( p.)ISBN: 83-7199-373-0.Detail