Difference between revisions of "Riccati equation"
From timescalewiki
| Line 2: | Line 2: | ||
$$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | ||
where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$. | where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$. | ||
| + | |||
| + | =Properties= | ||
| + | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| + | <strong>Theorem:</strong> STATEMENT OF THEOREM | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> proof goes here █ | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | =References= | ||
| + | [http://web.mst.edu/~bohner/papers/deotsas.pdf] | ||
Revision as of 22:42, 27 June 2015
Let $\mathbb{T}$ be a time scale. The Riccati equation is the nonlinear dynamic equation defined by $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$.
Properties
Theorem: STATEMENT OF THEOREM
Proof: proof goes here █
