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:
- Function Spaces and Integral Operators
- Nemytskij Operators in Spaces of Measurable Functions
- Nemytskij Operators in Spaces of Continuous Functions
- Fixed Point Theorems: Old and New
- Applications I
- 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.
