New existence results for prescribed mean curvature problem on balls under pinching conditions

We consider a kind of Yamabe problem whose scalar curvature vanishes in the unit ball ${\mathbb{B}}^n$ and on the boundary ${\mathbb{S}}^{n-1}$ the mean curvature is prescribed. By combining critical points at infinity approach with Morse theory we obtain new existence results in higher dimensional case $n\geq 5$, under suitable pinching conditions on the mean curvature function.