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This paper considers the prescribed zero scalar curvature and mean curvatureproblem on the n-dimensional Euclidean ball for $n \geq 3$. Given arotationally symmetric function $H:\partial B^{n}\rightarrow R$, in this work,we will prove that if $H'(r)$ changes signs where $H>0$ and $H(r)$ alsosatisfies a flatness condition then there exists a metric $g$ conformal to theEuclidean metric, with zero scalar curvature in the ball and mean curvature $H$on its boundary.

Conformal metrics on the ball with prescribed mean curvature on the boundary