Course Description

This is a continuation of MATH 516 (elementary linear PDEs), with the focus now on nonlinear PDEs. We will discuss variational, topological and other nonlinear methods for nonlinear differential equations, including the direct method of calculus of variations, mountain pass lemma, concentration compactness, method of moving planes, degree theory, Crandall-Rabinowitz bifurcation, monotonicity formula, and infinite dimensional Liapunov-Schmidt reduction method.

Lecture summaries and some references will be available in a public owncloud folder, whose link will be given to the audience. The link will expire on April 30, 2020.

Prerequisites

MATH 516 or equivalent. Other relevant materials will be reviewed during the course.

Topics

Here is the tentative outline. It can be adjusted according to audience background and interests.

References

More references will be added during the term.

Evaluation

The evaluation is based on homework assignments and class participation.

Instructor and lectures

Instructor: Dr. Tai-Peng Tsai, Math building room 109, phone 604-822-2591, ttsai at math.ubc.ca.

Lectures: Tue Thu 14:00-15:15pm, Math Annex MATX 1118
Update: Since Jan 17, we meet Mon Wed Fri 11:00-11:50am, MATH 203

Office hours: TBA, Mon Wed 1:30-2:20pm, and by appointment (Tsai's schedule).