Open Access Theses and Dissertations

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Brno University of Technology

1. Vážanová, Gabriela. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.

Degree: 2020, Brno University of Technology

URL: http://hdl.handle.net/11012/195761 

This thesis focuses on functional differential equations of mixed type also referred to as advance-delay equations. It gives sufficient conditions for the existence of global and semi-global solutions to nonlinear mixed differential systems. The methods used in this thesis consist of building suitable operators for differential equations and proving the existence of their fixed points. These fixed points are then used to construct the solutions of advance-delay equations. The monotone iterative method and Schauder-Tychonoff fixed point theorems are used in the proofs. In both cases, we also provide solution estimates. Moreover, with the monotone iterative method, these estimates may be improved by iterations. In addition, criteria for linear equations and systems are derived and series of examples are provided. The results obtained are also applicable to ordinary, delayed or advanced differential equations. Advisors/Committee Members: Diblík, Josef (advisor), Růžičková, Miroslava (referee), Fečkan,, Michal (referee).

Subjects/Keywords: funkcionální diferenciální rovnice smíšeného typu; zpožděný argument; předcházející argument; semi-globální řešení; globální řešení; monotónní iterační metoda; Schauderova-Tychonovova věta o pevném bodu; mixed-type functional differential equation; delayed argument; advanced argument; semi-global solution; global solution; monotone iterative method; Schauder-Tychonoff fixed point theorem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Vážanová, G. (2020). Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/195761

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Vážanová, Gabriela. “Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.” 2020. Thesis, Brno University of Technology. Accessed January 20, 2021. http://hdl.handle.net/11012/195761.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Vážanová, Gabriela. “Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.” 2020. Web. 20 Jan 2021.

Vancouver:

Vážanová G. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. [Internet] [Thesis]. Brno University of Technology; 2020. [cited 2021 Jan 20]. Available from: http://hdl.handle.net/11012/195761.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Vážanová G. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. [Thesis]. Brno University of Technology; 2020. Available from: http://hdl.handle.net/11012/195761

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Brno University of Technology

2. Piddubna, Ganna Konstantinivna. Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/30904 

This work is devoted to computing the solution, stability of the solution and controllability of respective system of linear matrix differential equation with delay x'(t)=A0x(t)+A1 x(t-tau), where A0, A1 are constant matrices and tau>0 is the constant delay. To solve this equation, the "step by step" method was used. The solution was found in recurrent form and in general form. Stability and the asymptotic stability of the solution of the equation was investigated. Conditions for stability were defined. The Lyapunov’s functional theory is basic for the investigation. Necessary and sufficient condition for controllability in same matrices case was defined and the control was built. Sufficient conditions for controllability in communicative matrices case and general case were defined and controls were built. All results were illustrated with non-trivial examples. Advisors/Committee Members: Baštinec, Jaromír (advisor), Růžičková, Miroslava (referee), Dzhalladova, Irada (referee).

Subjects/Keywords: diferenciální rovnice; systémy diferenciálních rovnic; rovnice se zpožděním; druhá Ljapunovova metoda; stabilita řešení; řiditelnost; zpožděný argument; differential equation; systems of differential equations; equations with delay; the second method of Lyapunov; stability of solution; controllability; delayed argument

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Piddubna, G. K. (2019). Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/30904

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Piddubna, Ganna Konstantinivna. “Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay.” 2019. Thesis, Brno University of Technology. Accessed January 20, 2021. http://hdl.handle.net/11012/30904.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Piddubna, Ganna Konstantinivna. “Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay.” 2019. Web. 20 Jan 2021.

Vancouver:

Piddubna GK. Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Jan 20]. Available from: http://hdl.handle.net/11012/30904.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Piddubna GK. Lineární maticové diferenciální rovnice se zpožděním: Linear Matrix Differential Equation with Delay. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/30904

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Brno University of Technology

3. Baštincová, Alena. Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/3027 

This dissertation discusses the solutions to the differential equation and to systems of differential equations. The main attention is paid to study of asymptotical properties of equations with delay and systems of equations with delay. In the first chapter are given physical and technical examples described by differential equations with delay and their systems. The classification of equations with delay is given and basic notions of theory of stability are formulated (mainly with the emphasis on the Lyapunov second method). In the second chapter estimates of solutions of equations of neutral type are studied. The third chapter deals with systems of differential equations of neutral type. Asymptotic estimates for solutions and their derivatives are proved. At the end of the chapter examples and comparisons of our results and of other authors are given. The calculation were performed with the MATLAB software. Last, the fourth chapter deals with asymptotical properties of systems having a special type of nonlinearities, so called ``sector nonlinearities''. Properties and estimations of solutions and derivatives are derived. The basic tools used in the dissertation are the Lyapunov second method and functionals of Lyapunov-Krasovskii type. Advisors/Committee Members: Diblík, Josef (advisor), Růžičková, Miroslava (referee), Dzhalladova,, Irada (referee).

Subjects/Keywords: diferenciální rovnice; systémy diferenciálních rovnic; rovnice neutrálního typu; druhá Ljapunovova metoda; funkcionál Ljapunova-Krasovského; stabilita řešení; zpožděný argument.; differential equation; systems of differential equations; equations of the neutral type; the second method of Lyapunov; functional Lyapunov-Krasovskii; stability of solution; delayed argument.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Baštincová, A. (2019). Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/3027

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Baštincová, Alena. “Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type.” 2019. Thesis, Brno University of Technology. Accessed January 20, 2021. http://hdl.handle.net/11012/3027.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Baštincová, Alena. “Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type.” 2019. Web. 20 Jan 2021.

Vancouver:

Baštincová A. Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Jan 20]. Available from: http://hdl.handle.net/11012/3027.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Baštincová A. Odhady řešení diferenciálních systémů se zpožděným argumentem neutrálního typu: Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/3027

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.