Difference between revisions of "Riccati equation"
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| − | Let $\mathbb{T}$ be a [[time scale]]. The Riccati equation is the nonlinear [[dynamic equation]] defined by | + | Let $\mathbb{T}$ be a [[time scale]]. The [[self-adjoint]] equation is $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$. The Riccati equation is the nonlinear [[dynamic equation]] defined by |
$$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | ||
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= | ||
| + | |||
| + | =References= | ||
| + | [http://web.mst.edu/~bohner/papers/deotsas.pdf] | ||
Latest revision as of 06:23, 10 June 2016
Let $\mathbb{T}$ be a time scale. The self-adjoint equation is $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$. 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 $t \in \mathbb{T}^{\kappa}$.
