Difference between revisions of "Delta exponential dynamic equation"
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(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: $$y^{\Delta}(t)=p(t)y(t), \quad...") |
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| − | + | Let $\mathbb{T}$ be a [[time scale]] and let $p \in$ [[Forward regressive function|$\mathcal{R}$]]$(\mathbb{T},\mathbb{C})$. The following [[dynamic equation]] is called the exponential dynamic equation: | |
| − | Let $\mathbb{T}$ be a [[time scale]] and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following [[dynamic equation]] | + | $$y^{\Delta}(t)=p(t)y(t).$$ |
| − | $$y^{\Delta}(t)=p(t)y(t) | + | |
| − | + | =Properties= | |
| + | |||
| + | =See also= | ||
| + | [[Delta exponential]]<br /> | ||
=References= | =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}}: $(2.17)$ |
| + | *{{PaperReference|The logarithm on time scales|2005|Martin Bohner|next=Euler-Cauchy logarithm}}: $(1)$ | ||
| + | |||
| + | [[Category:Definition]] | ||
Latest revision as of 17:02, 11 February 2017
Let $\mathbb{T}$ be a time scale and let $p \in$ $\mathcal{R}$$(\mathbb{T},\mathbb{C})$. The following dynamic equation is called the exponential dynamic equation: $$y^{\Delta}(t)=p(t)y(t).$$
Properties
See also
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): $(2.17)$
- Martin Bohner: The logarithm on time scales (2005)... (next): $(1)$
