# Nonlinear Analysis I and II

Copyright: © private## Nonlinear Analysis I

Nonlinear Analysis I is an elective course for bachelor students. Depending on current research interests, a selection of the following topics is presented: topological methods of nonlinear analysis, fixed-point theory, Morse theory, bifurcation theory, nonlinear problems on manifolds, nonlinear differential equations and continuous operator problems.

Topics

Students become familiar with modern methods and concepts for solving nonlinear and global problems in analysis and are introduced to the interplay of analysis and topology by studying several problems from the areas of differential geometry, nonlinear differential equations and mathematical physics.

Prerequisites

Prerequisites for taking the course are the modules Analysis I-III.

Exam

The examination consist of a written or oral exam; duration and type of the exam are announced at the beginning of the semester. For admission to the exam, a sufficient number of exercises has to be solved and submitted.

Literature

- J. Milnor, Topology from the Differentiable Viewpoint
- E. Zeidler, Nonlinear Functional Analysis
- C. Melcher, Nonlinear Analysis (Skript)

## Nonlinear Analysis II

During the course Nonlinear Analysis 2, the analytical difficulties behind physical and geometric problems are examined, the interplay of different analytical techniques in working on nonlinear problems is developed and modern analytical methods are adapted to given problems from physics and differential geometry.

Topics

Depending on current research interests, a selection of the following topics is covered: monotonous operators, topological methos of nonlinear analysis, Morse theory, nonlinear problems on manifolds and problems from fluid mechanics.

Exam

The examination consists of an oral or written exam, admission to the exam is gained by solving and submitting exercises during the semester.

Literature

Original works and research papers