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Bifurcation Theory (Summer Semester 2017)

This lecture is intended to give an introduction to bifurcation theory with applications in ordinary and partial differential equations. It is suitable for students with knowledge covered by one of the lectures Functional analysis or Boundary and Eigenvalue Problems or similar advanced courses in analysis. The course is open to both Bachelor and Master students.

The first lecture is on Tuesday, April 25th.
The first exercise session is on Wednesday, April 26th.

Exercise sheets will appear on a weekly basis, the first one will be handed out on Wednesday, April 26th. The exercise sheet may be returned for correction, but there is no obligation to do so.

Schedule
Lecture: Tuesday 15:45-17:15 SR 3.68
Problem class: Wednesday 15:45-17:15 SR 3.69
Lecturers
Lecturer PD Dr. Rainer Mandel
Office hours: by appointment
Room -1.019 Kollegiengebäude Mathematik (20.30)
Email: rainer.mandel@kit.edu
Problem classes Dr. Janina Gärtner
Office hours: Friday 10:00-11:00 and on appointment
Room 3.038 Kollegiengebäude Mathematik (20.30)
Email:
Problem classes Dr. Dominic Scheider
Office hours: on appointment
Room -1.021 Kollegiengebäude Mathematik (20.30)
Email: dominic.scheider@kit.edu

The content of this lecture is described in my post.


Problem Sheets

Problem Sheet 01 Solutions 01
Problem Sheet 02 Solutions 02
Problem Sheet 03 Solutions 03
Problem Sheet 04 Solutions 04
Problem Sheet 05 Solutions 05
Problem Sheet 06 Solutions 06
Problem Sheet 07 Solutions 07
Problem Sheet 08 Solutions 08
Problem Sheet 09 Solutions 09
Problem Sheet 10 Solutions 10
Problem Sheet 11 Solutions 11
Problem Sheet 12 Solutions 12

Examination

There will be oral exams.

References

  • Ambrosetti, Prodi: A Primer on Nonlinear Analysis
  • Ambrosetti, Malchiodi: Nonlinear analysis and semilinear elliptic problems
  • Chang: Methods in nonlinear analysis
  • Deimling: Nonlinear functional analysis (The Dover Books series)
  • Kielhöfer: Bifurcation Theory : An Introduction with Applications to Partial Differential Equations
  • Evans: Partial differential equations