Nonlinear Differential Equations (NMNV406) (Summer Semester 2022/2023)
This lecture course will cover the solution of nonlinear differential equations. Topics covered will include:
- Basic theorems from the theory of monotone and potential operators,
- Nonlinear differential equations in divergent form,
- Carathéodory's growth conditions, Nemycky operators,
- Variational methods and application of theory of monotone and potential operator, and proof of existence of solution,
- Numerical solution of nonlinear differential equations using the finite element method.
Exams:
The final exam will consist of a 30 minute oral examination on the topics covered.
Lectures:
- Monday 09:00 – 10:30, K7 Sokolovská 83 Karlín
Practicals:
- Monday 10:40 – 12:10, K7 Sokolovská 83 Karlín
Suggested Reading:
- K. Böhmer, Numerical Methods for Nonlinear Elliptic Differential Equations, Oxford University Press, 2010.
- V. Dolejší & K. Najzar, Nelineární funkcionální analýza, matfyzpress, 2011.
- E. Ziedler. Nonlinear functional analysis and its applications I, Springer, 1984.
- E. Ziedler. Nonlinear functional analysis and its applications II/A, Springer, 1990.
- J. Nečas. Introduction to the Theory of Nonlinear Elliptic Equations, Wiley, 1986
- L. C. Evans, Partial Differential Equations, AMS, 2010.