Difference between revisions of "Delta exponential dynamic equation"
From timescalewiki
(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following dynamic equation holds: $$y^{\Delta}(t)=p(t)y(t), \quad...") |
|||
| Line 4: | Line 4: | ||
is called the exponential dynamic equation. Its solution is the [[delta exponential]]. | is called the exponential dynamic equation. Its solution is the [[delta exponential]]. | ||
| − | =References= | + | ==Proof== |
| + | |||
| + | ==References== | ||
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Semigroup property of delta exponential|next=findme}}: $(2.17)$ | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Semigroup property of delta exponential|next=findme}}: $(2.17)$ | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 23:18, 8 February 2017
Theorem
Let $\mathbb{T}$ be a time scale and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following dynamic equation holds: $$y^{\Delta}(t)=p(t)y(t), \quad y(s)=1$$ is called the exponential dynamic equation. Its solution is the delta exponential.
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): $(2.17)$
