The solution manifold and C1-smoothness for differential equations with state-dependent delay

By H. Walther. 2003

185 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/db9b20b3afd7b1056f51fcccd1c716db2504a68b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. A. Rezounenko
2. John Mallet-Paret
3. Roger D. Nussbaum
4. Tibor Krisztin
5. Jianhong Wu
6. Shangjiang Guo

In Computational Theory and Mathematics

1. A. Rezounenko
2. Roger D. Nussbaum
3. John Mallet-Paret
4. Jianhong Wu
5. Tibor Krisztin
6. Shigui Ruan
7. Emilia M. Fridman

In Control and Systems Engineering

1. A. Rezounenko
2. Tibor Krisztin
3. John Mallet-Paret
4. Roger D. Nussbaum
5. Jianhong Wu
6. Ferenc Hartung
7. Shigui Ruan
8. Emilia M. Fridman

Citations in the corpus

• A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors (2006, background): “Both authors wish to thank Canada Research Chairs Program and the Natural Sciences and Engineering Research Council of Canada for the financial support, and both authors would like to thank Hans-Otto Walther for bringing state-dependent delay differential equations to our attention during our visit ”
• Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions (2008, background): “…a new class of delay equations - equations with a state-dependent delay (SDD) attracts much attention of researchers (see e.g. [Walther (2002), Walther (2003), Nussbaum and Mallet-Paret (1992), Nussbaum and Mallet-Paret (1996), Mallet-Paret et al. (1994), Krisztin (2003), Walther (2007)] and…”
• Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations (2011, methodology): “In this direction we mention the recent foundational work of Walther [51], Hartung, Krisztin, Walther, and Wu [25], and Krisztin [28] [29].”
• Smoothness Properties of Semiflows for Differential Equations with State-Dependent Delays (2004, methodology): “Using the fact that ae(`) does not depend on `2, one easily finds that Xf 6 ;. In [ 9 ] we saw that f has the properties (P1) and (P2).”
• Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold (2014, methodology): “In this work we combine the results for ODEs [8,16,27] and PDEs [22,24].”