Juergen Appell : Nonlinear operators in function spaces

The purpose of the seminar is to provide a variety of existence and uniqueness results for solutions of nonlinear problems arising in mathematics, mechanics, physics, and engineering. This amounts to studying certain analytical properties of both linear and nonlinear operators in various function spaces which frequently occur in applications, such as Lebesgue, Orlicz, Sobolev, Chebyshev, and Hoelder spaces.

The seminar will consist of 6 lectures covering (more or less) the following topics:

  1. Function Spaces and Integral Operators
  2. Nemytskij Operators in Spaces of Measurable Functions
  3. Nemytskij Operators in Spaces of Continuous Functions
  4. Fixed Point Theorems: Old and New
  5. Applications I
  6. Applications II
The exposition will be rather elementary, building more on illuminating examples and counterexamples than on abstract theorems. It should therefore be accessible to postdoc and PhD students with a standard background in functional analysis and operator theory.