A Liouville-Type Theorem of the Linearly Perturbed Paneitz Equation on <i>S</i>3

Abstract We prove a Liouville-type theorem for the linearly perturbed Paneitz equation: For $\epsilon&amp;gt;0$ small enough, if $u_\epsilon $ is positive smooth solution of $$ \begin{align*} &amp;P_{S^3} u_\epsilon+\epsilon u_\epsilon=-u_\epsilon^{-7} \qquad \textrm{on}\ S^3,\end{align*}$$where $P_{S^3}$ operator round metric $g_{S^3}$, then constant. This confirms conjecture proposed by Hang and Yang in [6].