Difference between revisions of "Generalized zero"
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Let $\mathbb{T}$ be a [[time scale]]. Let $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$ be a [[self-adjoint]] equation. We say that a solution $y$ of the self-adjoint equation has a generalized zero at $t$ if $y(t)=0$ or if $t$ is left-scattered and the following formula holds: $p(\rho(t))y(\rho(t))y(t)<0$. | Let $\mathbb{T}$ be a [[time scale]]. Let $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$ be a [[self-adjoint]] equation. We say that a solution $y$ of the self-adjoint equation has a generalized zero at $t$ if $y(t)=0$ or if $t$ is left-scattered and the following formula holds: $p(\rho(t))y(\rho(t))y(t)<0$. | ||
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Latest revision as of 15:28, 21 January 2023
Let $\mathbb{T}$ be a time scale. Let $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$ be a self-adjoint equation. We say that a solution $y$ of the self-adjoint equation has a generalized zero at $t$ if $y(t)=0$ or if $t$ is left-scattered and the following formula holds: $p(\rho(t))y(\rho(t))y(t)<0$.
