On the positive solutions for a perturbed negative exponent problem on \begin{document} $\mathbb{R}^3$ \end{document}

In this paper, we study the following fourth order elliptic problem with a negative nonlinearity : \begin{document}$\begin{align}\left\{\begin{aligned} Δ^2 u&=-\frac{15}{16}(1+ \varepsilon Q)u^{-7} &&\text{ in } \mathbb R^3\\ u &>0 &&\text{ in } \mathbb R^3,\\ u(x) &\sim |x| \text{ as }{|x|\to ∞}. & \end{aligned} \right.\end{align}$ \end{document} Here \begin{document} $Q$ \end{document} is a \begin{document} $C^{1}$ \end{document} bounded function on \begin{document} $\mathbb{R}^3$ \end{document} and \begin{document} $\varepsilon >0$ \end{document} is a small parameter. We prove the existence, uniqueness of positive solutions for the above perturbed fourth order problem.