The lectures will start from 9:00 to 11:30 in the morning and from 14:00 to 16:30, including 30 minutes break in between. The tentative schedule is as follows:

Delay differential equations
T. Krisztin (Bolyai Institute, University of Szeged, Hungary)

1. Introduction. Basic theory
Examples for time delayed systems
Basic properties
Existence, uniqueness, continuous dependence
Continuation: forward, backward
Differentiability
2. Linear equations
Generator, spectrum
Decomposition of the phase space
Variation of constants formula
Linearization
3. Nonlinear equations
Delayed monotone feedback
Global attractor
Unstable sets of equilibria
Periodic orbits, connecting orbits
4. Different research topics
Nonmonotone feedback
State-dependent delays
Problems

References:
- H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer, 2011.
- T. Krisztin, H.-O. Walther, J. Wu, Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive feedback, Fields Institute Monographs, AMS, 1999.
- O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel, H.-O. Walther, Delay Equations, Springer, 1995.
- J. K. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, 1993.
- F. Hartung, T. Krisztin, H.-O. Walther, J. Wu, Functional differential equations with statedependent delay: theory and applications, In: Handbook of differential equations: Ordinary differential equations. Vol. 3. Elsevier; North-Holland, 2006. pp. 435-545.