| Course Unit Code | 470-4115/03 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type B |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
| Summary |
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| The subject contains basic concepts of nonlinear functional analysis (compact operators, implicit function theorem, topological degree, monotone operators). |
| Learning Outcomes of the Course Unit |
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| Successful student will gain basic knowledge of nonlinear functional analysis and its applications. |
| Course Contents |
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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. |
| Recommended or Required Reading |
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| Required Reading: |
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E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.
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P. Drábek, A. Kufner: Úvod do funkcionální analýzy, ZČU, Plzeň, 1993.
P. Drábek, A. Kufner: Funkcionální analýza, ZČU, Plzeň, 1994.
S. Fučík, A. Kufner: Nonlinear differential equations, Elsevier, Amsterdam, 1980.
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| Recommended Reading: |
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| E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995. |
S. Fučík, A. Kufner: Nelineární diferenciální rovnice, SNTL, Praha, 1978.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 10 |
| Examination | Examination | 70 | 21 |