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Course, academic year 2019/2020
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Nonlinear Functional Analysis 2 - NMMA502
Title in English: Nelineární funkcionální analýza 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Stanislav Hencl, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Povinné
Classification: Mathematics > Functional Analysis
Annotation -
Last update: T_KMA (02.05.2013)
Mandatory course of the master study branch Mathematical analysis. Recommended for the second year of master studies. Content: Mountain pass lemma, topological degree, Leray-Schauder degree, monotone operators in a Hilbert space, nonlinear semigroups, bifurcations.
Course completion requirements - Czech
Last update: prof. RNDr. Jiří Spurný, Ph.D., DSc. (10.05.2018)

Zápočet bude udělován za nadpoloviční účast na cvičeních.

Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Literature - Czech
Last update: T_KMA (02.05.2013)

P. Drábek, J. Milota: Methods of nonlinear analysis. Applications to differential equations. Birkhäuser Verlag, Basel, 2007.

L. C. Evans: Partial differential equations. AMS, Providence, RI, 2010

Requirements to the exam - Czech
Last update: prof. RNDr. Jan Malý, DrSc. (01.03.2018)

Zkouška je ústní. Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu, jak byl presentován na přednášce.

Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (09.06.2015)

1. Weak convergence in L_1

characterization, biting lemma

2. Problems convex in the last variable

3. Generalized convexity (briefly)

rank-1 convexity, polyconvexity, kvaziconvexity

4. Mountain pass lemma

Ekeland variational principle, Palais-Smale condition

5. Nonlinear semigroup

6. Bifurcation

Crandall-Rabinowitz theorem, bifurcation from the point of spectrum with odd multiplicity, variational problem and bifurcation from the point of a spectrum with even multiplicity

Entry requirements -
Last update: prof. RNDr. Jiří Spurný, Ph.D., DSc. (10.05.2018)

Elements of linear functional analysis, elements of measure theory, theory of Lebesgue integral, function spaces.

 
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