Assume that the function $\xi_{k}(z)$ satisfies the following property: there are $\eta_{0}\in(-\delta_{b}/2,\delta_{b}/2)$, a sequence of positive constants $\mathfrak{B}_{k}>0$ such that

(5.206)

$$|\xi_{k}(z)|\leq\mathfrak{B}_{k}\cdot e^{\eta_{0}\cdot z^{\frac{n}{2}}}.$$

Let $u_{k}(z)$ be the particular solution (5.204), then there exists some constant $C_{0}>0$ such that the particular solution $u_{k}$ satisfies the uniform estimate

(5.207)

$$|u_{k}(z)|\leq C_{0}\cdot\mathfrak{B}_{k}\cdot(\Lambda_{k})^{\frac{1}{2n}}\cdot e^{\eta\cdot z^{\frac{n}{2}}}$$

for any $\eta>\eta_{0}$.