KMA/NDR Nonlinear Differencial Equations

Lecturer: Tomáš Fürst
Lecture: 2 hours/week e exercise 2 hours/week
Credits: 4
Summer semester
Form of course completion: course credit, exam

A. The language of dynamical systems

• A summary of linear systems
• De-motivation: Chaos and the Lorenz attractor
• Case-study: Driven damped oscillations
• Relation of non-linear to linear systems: The Hartman-Grobman Theorem
• Chaos forbidden: The Poincare-Bendixon Theorem

B. Fixed-point methods

• Fixed-point theorems
• Standard applications
• BVP for nonlinear ODEs
• Nonlinear PDEs: Classical approach
• Nonlinear PDEs: Modern approach
• Modern approach to nonlinear evolution PDEs.

C. Monotonicity methods

• Monotonicity and the Browder-Minty Theorem
• Application: The method of lower and upper solutions
• Pseudo-monotonicity and the Brezis Theorem
• Application to steady state problems
• Application to evolution problems