Ordinary differential equations

First published in
Operator theory 
Number in series
287
Start Page
51
End Page
66
Citation
Operator Theory: Advances and Applications 287: 51-66 (2022)
Publisher DOI
10.1007/978-3-030-89397-2_4
Scopus ID
2-s2.0-85124378837
Publisher
Springer
In this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem. It is also called existence and uniqueness theorem for initial value problems for ordinary differential equations as well as Cauchy–Lipschitz theorem). We shall furthermore see that the abstract theory developed here also allows for more general differential equations to be considered. In particular, we will have a look at so-called delay differential equations with finite or infinite delay; neutral differential equations are considered in the exercises section.
DDC Class
510: Mathematik