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- Academic unit or major
- Mathematics
- Instructor(s)
- Onodera Michiaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H137)
- Group
- -
- Course number
- ZUA.C332
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 2Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
We study the implicit function theorem, bifurcation theory and variational methods.
This course is following Advanced courses in Analysis A.
Student learning outcomes
Understanding of the basic theory of nonlinear functional analysis including the implicit function theorem, bifurcation theory and variational methods
Keywords
elliptic partial differential equations, functional analysis, implicit function theorem, bifurcation theory, variational methods
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. Occasionally I will give problems for reports.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Implicit function theorem | Details will be provided during each class session. |
| Class 2 | Bifurcation theory 1 | Details will be provided during each class session. |
| Class 3 | Bifurcation theory 2 | Details will be provided during each class session. |
| Class 4 | Deformation lemma | Details will be provided during each class session. |
| Class 5 | Mountain pass lemma | Details will be provided during each class session. |
| Class 6 | Symmetry and Compactness | Details will be provided during each class session. |
| Class 7 | Concentration-compactness principle | Details will be provided during each class session. |
| Class 8 | Other topics | Details will be provided during each class session. |
Textbook(s)
None
Reference books, course materials, etc.
- K. Masuda, Nonlinear mathematics (in Japanese), Asakura Shoten, 1985.
- M. Willem, Minimax Theorems, Birkhauser, 1996.
Assessment criteria and methods
Report (100%)
Related courses
- ZUA.C331 ： Advanced courses in Analysis A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis A (ZUA.C331).
Other
None
