Infinitely many solutions for the prescribed boundary mean curvature problem on ${\mathbb{B}}^N$

Abstract

We consider the following prescribed boundary mean curvature problem in ${\mathbb{B}}^N$ with the Euclidean metric $-\hat{I}”u=0$, $u>0$ in $B^N,\frac{\partial u}{\partial \hat{I}½}+\frac{N-2}{2}u=\frac{N-2}{2}K(x)u^{N/(N-2)}$ on $S^{N-1},where$K$ispositiveandrotationallysymmetricon$\mathbb S^{N-1}$.Weshowthatif${K}$hasalocalmaximumpoint,thentheequationhas\mathbf{infinitelymanypositive}solutions,whicharenon-radialon$\mathbb S^{N-1}$.

arXiv admin note: text overlap with arXiv:0804.4030 by other authors