Difference between revisions of "Delta exponential dynamic equation"

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==Theorem==
+
Let $\mathbb{T}$ be a [[time scale]] and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following [[dynamic equation]] is called the exponential dynamic equation.
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==
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=Properties=
  
==References==
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=See also=
 +
[[Delta exponential]]<br />
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 +
=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:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Revision as of 23:20, 8 February 2017

Let $\mathbb{T}$ be a time scale and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following dynamic equation is called the exponential dynamic equation.

Properties

See also

Delta exponential

References