Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
We study the topological degree, the implicit function theorem, and the bifurcation theory.
This course is following Advanced topics in Analysis E1.
Understanding of the basic theory of nonlinear functional analysis including the topological degree, the implicit function theorem and the bifurcation theory
elliptic partial differential equations, functional analysis, topological degree, implicit function theorem, bifurcation theory
|✔ 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||- Topological degree theory 1 - Topological degree theory 2 - Implicit function theorem - Bifurcation theory 1 - Bifurcation theory 2 - Other topics||Details will be provided during each class.|
Enough preparation and review if necessary
- K. Masuda, Nonlinear mathematics (in Japanese), Asakura Shoten, 1985.
- L. Nirenberg, Topics in Nonlinear Functional Analysis (Courant Lecture Notes), AMS, 2001.