We study the $L^1-L^{\infty }$ dispersive estimate of the inhomogeneous fourth-order Schrödinger operator $H={\Delta }^2-\Delta +V\left(x\right)$ with zero energy obstructions in ${\mathbf{R}}^3$. For the related propagator $e^{-itH}$, we prove that for $0<\left|t\right|\le 1$, then $e^{-itH}{P}_{ac}\left(H\right)$ satisfies the ${\left|t\right|}^{-3∕4}$-dispersive estimate. For $\left|t\right|>1$, we prove that:  (1) if zero is a regular point of $H$, then $e^{-itH}{P}_{ac}\left(H\right)$ satisfies the ${\left|t\right|}^{-3∕2}$-dispersive estimate.  (2) If zero is purely a resonance of $H$, there exists a time dependent operator ${\mathcal{F}}_t$ such that $e^{-itH}{P}_{ac}\left(H\right)-{\mathcal{F}}_t$ satisfies the ${\left|t\right|}^{-3∕2}$-dispersive estimate.  (3) If zero is purely an eigenvalue or zero is both an eigenvalue and a resonance of $H$, then there exists a time dependent operator ${\mathcal{G}}_t$ such that $e^{-itH}{P}_{ac}\left(H\right)-{\mathcal{G}}_t$ satisfies the ${\left|t\right|}^{-3∕2}$-dispersive estimate. Here ${\mathcal{F}}_t$ and ${\mathcal{G}}_t$ satisfy the ${\left|t\right|}^{-1∕2}$-dispersive estimate.

我们研究 ${\mathrm{大号}}^{\mathrm{1个}}-{\mathrm{大号}}^{\infty }$ 非均匀四阶Schrödinger算子的色散估计 $H={\Delta }^2-\Delta +V（X）$ 零能量阻碍 ${\mathbf{[R}}^3$。对于相关的传播者${Ë}^{-\mathrm{一世}ŤH}$，我们证明 $0<\left|Ť\right|\le \mathrm{1个}$， 然后 ${Ë}^{-\mathrm{一世}ŤH}{P}_{\mathrm{一个}C}（H）$ 满足 ${\left|Ť\right|}^{-3∕4}$-分散估计。为了$\left|Ť\right|>\mathrm{1个}$，我们证明：  （1）如果零是的正则点$H$， 然后 ${Ë}^{-\mathrm{一世}ŤH}{P}_{\mathrm{一个}C}（H）$ 满足 ${\left|Ť\right|}^{-3∕2}$-分散估计。  （2）如果零纯粹是的共振$H$，存在一个与时间有关的运算符 ${\mathcal{F}}_{Ť}$ 这样 ${Ë}^{-\mathrm{一世}ŤH}{P}_{\mathrm{一个}C}（H）-{\mathcal{F}}_{Ť}$ 满足 ${\left|Ť\right|}^{-3∕2}$-分散估计。  （3）如果零纯粹是一个特征值或零既是特征值又是共振$H$，则存在一个时间相关的运算符 ${\mathcal{G}}_{Ť}$ 这样 ${Ë}^{-\mathrm{一世}ŤH}{P}_{\mathrm{一个}C}（H）-{\mathcal{G}}_{Ť}$ 满足 ${\left|Ť\right|}^{-3∕2}$-分散估计。这里${\mathcal{F}}_{Ť}$ 和 ${\mathcal{G}}_{Ť}$ 满足 ${\left|Ť\right|}^{-\mathrm{1个}∕2}$-分散估计。