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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

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 (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

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