Existence of solutions for an approximation of the Paneitz problem on spheres

Abstract

This paper is devoted to studying the nonlinear problem with subcritical exponent $(S_{\varepsilon}) : \Delta^{2}u-c_n\Delta u+d_nu = Ku^{\frac{n+4}{n-4}-\varepsilon}$, $u$ on $ S^n$, where $n\geq5$, $ \varepsilon$ is a small positive parameter and $K$ is a a smooth positive function on $S^n$. We construct some solutions which blow up at $q$ different critical points of $K$.