SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Nonlinear Functional Analysis - NMNV402
Title: Nelineární funkcionální analýza
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Miloslav Vlasák, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Volitelné
M Mgr. NVM
M Mgr. NVM > Povinné
Classification: Mathematics > Functional Analysis
Incompatibility : NRFA018
Interchangeability : NMNV406, NRFA018
Is interchangeable with: NRFA018
Annotation -
Basic techniques of existence proofs of nonlinear operator solutions in Banach and Hilbert spaces. Teory of monotone, pseudomonotone and potential operators. Abstract numerical methods for solving nonlinear operator equations.
Last update: T_KNM (02.04.2015)
Course completion requirements -

Oral examination of topics discussed at the lectures

Last update: Congreve Scott, Ph.D. (27.04.2020)
Literature -

DOLEJŠÍ V., NAJZAR K. Nelineární funkcionální analýza, 2011, skripta MFF UK, 202 s. ISBN 978-80-7378-137-8

FRANCŮ J. Úvod do teorie monotónních operátorů, 1987, skripta VUT Brno

FUČÍK S., NEČAS J., SOUČEK J., SOUČEK V. Spectral analysis of nonlinear operators, 1973, Springer ISBN 978-3-540-06484-8

ZEIDLER E. Nonlinear functional analysis and its applications I, 1984, Springer

PASCALI D., SBURLAN S. Nonlinear mappings of monotone type, 1978,  Editura academiei, x 341 s., ISBN 90-286-0118-X

Last update: T_KNM (15.09.2013)
Requirements to the exam -

Oral examination of topics discussed at the lectures

Last update: Vlasák Miloslav, RNDr., Ph.D. (26.02.2018)
Syllabus -

Resuming basics from functional analysis.

Existence theorem.

Theory of monotone operators, pseudomonotone operators.

Generalisations of existence theorem.

Theory of potential operators.

Abstract numerical methods for solving nonlinear operator equations.

Last update: T_KNM (15.09.2013)
Entry requirements -

Basic knowledge of functional analysis.

Last update: Vlasák Miloslav, RNDr., Ph.D. (12.05.2018)
 
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