Nonlinear Functional Analysis - NRFA018
Title: Nelineární funkcionální analýza
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~dolejsi/Vyuka/index.htm
Guarantor: RNDr. Miloslav Vlasák, Ph.D.
Classification: Mathematics > Functional Analysis
Interchangeability : NMNV402
Is incompatible with: NMNV402
Is interchangeable with: NMNV402
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Annotation -
The course represents the treatment of basic results from nonlinear functional analysis in Banach spaces. It contains: monotone operators, fixed point theory (Brouwer's and Schauder's fixed point theorems), differentiability, potential operators, topological degree and numerical methods for solving nonlinear operator equations in Banach spaces.
Last update: DOLEJSI/MFF.CUNI.CZ (15.04.2008)
Aim of the course -

The course gives students a knowledge of fundamentals of the differential calculus in Banach spaces, theory of monotone and potential operators and numerical methods for the solution of operator equations.

Last update: T_KNM (16.05.2008)
Literature -

Gajewski H., Gröger K., Zacharias K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Berlín l974, (ruský překlad l978)

Fučík Sv., Nečas J., Souček J., Souček V.: Spectral analysis of nonlinear operators, l973

Deimling K.: Nonlinear functional analysis, l985

Zeidler E.: Nonlinear Functional Analysis and Its Applications l, l984

Last update: T_KNM (16.05.2008)
Teaching methods -

Lectures in a lecture hall.

Last update: T_KNM (16.05.2008)
Requirements to the exam -

Examination according to the syllabus.

Last update: T_KNM (16.05.2008)
Syllabus -

Introduction in the theory of diferential calculation in Banach spaces.

Browder's theory of monotone operators.

Potential operators.

Dual functionals.

Numerical methods for operatoe equations, Galerkin and Ritz methods.

Brower's and Schauder's fixed-point theorems.

Last update: T_KNM (16.05.2008)
Entry requirements -

basic knowledge of functional analysis

Last update: T_KNM (16.05.2008)