Colloquium on October 12, 2009

Hans-Otto Walther
Universität Gießen

State-dependent delays: Framework, results, open problems

We motivate and present a framework for the investigation of differential equation with state-dependent delays, with the natural state space determined by the equation itself. The theory covers equations where the delay is given by the state and its history only implicitly, as in various examples based on physics. Recent results concern equations of neutral type. We also report about applications and describe open problems which seem related to lack of smoothness.