SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Nonlinear Functional Analysis - NMNV402
Title in English: Nelineární funkcionální analýza
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016 to 2018
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: 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 : NRFA018
Annotation -
Last update: T_KNM (02.04.2015)
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.
Course completion requirements -
Last update: RNDr. Miloslav Vlasák, Ph.D. (26.02.2018)

The condition for the credit is an active participation at exercices. The nature of the condition excludes the repetition of this check.

Literature -
Last update: T_KNM (15.09.2013)

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

Requirements to the exam -
Last update: RNDr. Miloslav Vlasák, Ph.D. (26.02.2018)

Oral examination of topics discussed at the lectures

Syllabus -
Last update: T_KNM (15.09.2013)

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.

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

Basic knowledge of functional analysis.

 
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