Let $A=\{ x\in \R^{ 2m} : 0< a< |x| <b\}$ be an annulus. Consider the following singularly perturbed elliptic problem on $A$ \begin{ equation} \begin{ array}{ lll} -\eps^2{ \De u} + |x|^{ \eta}u = |x|^{ \eta}u^p, &\mbox{ \qquad in} A \notag u>0 &\mbox{ \qquad in} A u = 0 &\mbox{ \qquad on} \partial A \end{ array} %\label{ a1} \end{ equation} $1<p<2^*-1$. We shall prove the existence of a positive solution $u_\eps$ which concentrates on two different orthogonal spheres of dimension $(m-1)$ as $\eps\to 0$. We achieve this by studying a reduced problem on an annular domain in $\R^{ m+1}$ and analyzing the profile of a two point concentrating solution in this domain.
Categories: math.AP