Book chapter
Appendix C: Differential Equations
Dynamics with Inequalities, pp.353-359
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.appc
Abstract
We will consider here differential equation initial value problems of the form
d
x
d
t
(
t
)
=
ƒ
(
t
,
x
(
t
)
)
,
x
(
t
0
)
=
x
0
∈
X
,
C.1
where X is a given Banach space. We take this to mean that dx/dt exists almost everywhere, x(⋅) is an absolutely continuous function,
d
x
/
d
t
(
t
)
=
ƒ
(
t
,
x
(
t
)
)
for almost all t, and finally that
x
(
t
0
)
=
x
0
. This understanding of what a solution of a differential equation is derives from the work of Carathéodory; we say that such a function is a solution in the sense of Carathéodory.
Details
- Title: Subtitle
- Appendix C: Differential Equations
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Dynamics with Inequalities, pp.353-359
- Publisher
- Society for Industrial and Applied Mathematics
- Series
- Other Titles in Applied Mathematics
- DOI
- 10.1137/1.9781611970715.appc
- Language
- English
- Date published
- 01/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984242340802771
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