470-4115/03 – Nonlinear Functional Analysis (NEFN)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

Successful student will gain basic knowledge of nonlinear functional analysis and its applications.

Teaching methods

Lectures
Tutorials

Summary

The subject contains basic concepts of nonlinear functional analysis (compact operators, implicit function theorem, topological degree, monotone operators).

Compulsory literature:

E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.

Recommended literature:

E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.

Way of continuous check of knowledge in the course of semester

Tests, individual work.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Spectral Theory of Bounded Operators: Self - Adjoint Operators. Compact Operators. Fundamental Theorems of Nonlinear Functional Analysis: Baire Theorem. Open Mapping Theorem. Implicit Function Theorem. Bifurcation Theorem. Topological Methods: Brouwer Fixed Point Theorem. Topological Degree. Monotone Operators. Variational Methods: Ekeland Variational Principle. Mountain Pass Theorem. Saddle Point Theorem.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 2 Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner