Return to search

Věty o pevném bodě v teorii diferenciálních rovnic / Fixed point theorems in the theory of differential equations

This thesis is devoted to show various applications of fixed point theorems on dif- ferential equations. In the beginning we use a notion of topological degree to derive several fixed points theorems, primarily Brouwer, Schauder and Kakutani-Ky Fan the- orem. Then we apply them on a wide range of relatively simple problems from ordinary and partial differential equations (ode and pde). Finally, we take a look on a few more complex problems. First is an existence of a solution to the model of mechanical os- cillator with non-monotone dependence of both displacement and velocity. Second is a solution to so called Gause predator-prey model with a refuge. The last one is cer- tain partial differential equation with a constraint which determines maximal monotone graph. 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:415504
Date January 2020
CreatorsZelina, Michael
ContributorsPražák, Dalibor, Bárta, Tomáš
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

Page generated in 0.0019 seconds