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Bifurcation of ordinary differential equations from points of Fučík spektrum
Exnerová, Vendula ; Stará, Jana (advisor) ; John, Oldřich (referee)
Title: Bifurcation of Ordinary Differential Equations from Points of Fučík Spectrum Author: Vendula Exnerová Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Jana Stará, CSc., Department of Mathematical Analysis MFF UK, Prague Abstract: The main subject of the thesis is the Fučík spectrum of a system of two differential equations of the second order with mixed boundary conditions. In the first part of the thesis there are described Fučík spectra of problems of a differential equation with Dirichlet, mixed and Neumann boundary conditions. The other part deals with systems of two differential equations. It attends to basic properties of systems and their nontrivial solutions, to a possibility of a reduction of number of parameters and to a dependance of a problem with mixed boundary condition on one with Dirichlet boundary conditions. The thesis takes up the results of E. Massa and B. Ruff about the Dirichlet problem and improves some of their proofs. In the end the Fučík spectrum of a problem with mixed boundary conditions is described as the union of countably many continuously differentiable surfaces and there is proven that this spectrum is closed.
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Banach Function Spaces
Marko, Ján ; John, Oldřich (referee) ; Pick, Luboš (advisor)
N'a/ev prace: Banarhovy prostory fuiikci Autor: Jan Marko Katcdr;i: KaTedra inaleniaticke analy/y Yedouci bakalarske prace: doc1. UN Dr. Lubus Pick. CSc.. DSc. t'-inail vedoudho: Lubos.Pick'i'inff.cuni.c/ Abst.ra.kt.: V t.ejto ])riici su popisane xakladne vlastnosti Baimchovho priostoru funkcii. jeho podpriestor funkfii s absolutnc spujitou iiorniou a asociovany Banai-liov priestor I'luikcii. Zaobcra sa lie/ problcinal.ikou Lcbcsgucovycli pricslorov ['unkcii. branycli ako Banadiovo priest ory funkcif. \ Icxte su vyprarovaiu'1 priklady lykajuce sa.vlastnosti niicr ineratel'nych priosl.orov a k-h vplyv na ist udovanc'1 podpricstory. Taklio/ su vypracovaiK'1 priklady Baiia- chovyi'li iiorioni. iin ])n'sliisiio limiacliovc priest ory funkfii a. ich /;ikladne. N'la Klfcova slova: Banacliuva noriiia. Banacliov prieslor I'uukcif, asociovany prieslor. spojita noriua Title: Banach funct ion spaces Author: Jan Marko Department: Department of Mathematical Analysis Supervisor: doc. HNDr. Lubus Pick, CSc.. DSc. 'rvisor's e-mail address: Lubos.Pick'imir.cuni.cx Abstract: This thesis describes basic properties of Banach function spaces, its subspace of functions of absolutely continuous norm and its associa.lt; space.. II.also deals with problems of Lebesgue spaces considered to be Banach function spaces. Several problems...
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Difference equations and their applications in economical models
Ivanková, Kristýna ; Bárta, Tomáš (referee) ; John, Oldřich (advisor)
Ndzev prdc.e: Diferencni rovnice a jejich vyuziti v ekononrickych modelech Autor: Kristyna. Ivankova Katedra (uxtav): Katedra matematicke analyzy Vedouei bakaldrske prdce: Doc.RNDr. Oldfich John, C/Sc. e-mail vedouciho: jorm@karlin.mff.cuni.cz Abstrakt: V praci studujeiue linearni diferencni rovnice prvniho fadu a je- jich vyuziti pfi fonnulaci a liledani feseni inikroekononiickych a niakroekono- mickycli inodclu. Modoly, ktere v praci uvadinio, jsou natolik zjednodusenc, aby byio inoznc ziskat jojich fesoni poinoci zkounianeho niateniatickeho aparatu. U dii'ereiicnich rovnic sc xaniefinie na feseni iechto rovnic pro spccialni prave strany. Ziskane vysledky nasledno pouzijcme v inikroeko- nomickycli modelcch rovnuvahy trim. Zakladnim inodelein je zdc pavuci- novy model, z nej jsou odvozeuy uiodoly s noririalni cenou a a adaptivninii ocekavanimi. V zavern prace so zabyvame zkoiiirianim stability a dynamiky multiplikatoru v inakroekononiickych modelcch uzavfenc ekonomiky (rnodely zdaneni, spofeiii a zvyky spotrebitelu) i otevfeue ekonomiky. Kltcovd slova: linearni dilerencni rovnice, ekonoinicke modely, pavucinovy model, mnltiplikatory, stabilHa feseni Title: DifTerence oquaLioiis and their upplic.ations in economical models Author: Kristyna Ivankova. Department: Department of mathematical analysis...
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