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.
Understanding of the basic theory of nonlinear functional analysis including the implicit function theorem, bifurcation theory and variational methods
elliptic partial differential equations, functional analysis, implicit function theorem, bifurcation theory, variational methods
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course. Occasionally I will give problems for reports.
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. |
None
- K. Masuda, Nonlinear mathematics (in Japanese), Asakura Shoten, 1985.
- M. Willem, Minimax Theorems, Birkhauser, 1996.
Report (100%)
Students are required to complete Advanced courses in Analysis A (ZUA.C331).
None