470-4115/02 – Nonlinear Functional Analysis (NEFN)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 2 | Semester | winter |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | 2023/2024 |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
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.
Additional study materials
Way of continuous check of knowledge in the course of semester
Podmínky udělení zápočtu:
Aktivní účast na cvičeních. Vyřešení zadaných problémů.
E-learning
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.