Project detail

Limit properties of solutions of differential equations

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 English
The 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.

Keywords
asymptotické vlastnosti, obyčejné diferenciální rovnice, funkcionální diferenciální rovnice

Key words in English
asymptotic properties; ordinary differential equations; functional differential equations

Mark

IAA1163401

Default language

Czech

People responsible

Čermák Jan, prof. RNDr., CSc. - fellow researcher
Došlá 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