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arXiv · 1309.5755

On the solutions of a singular elliptic equation concentrating on two orthogonal spheres

B. B. Manna·P. N. Srikanth
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Abstract

Let $A=\{x\in \R^{2m} : 0< a< |x| 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.

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B. B. Manna, P. N. Srikanth. 2013-09-23. On the solutions of a singular elliptic equation concentrating on two orthogonal spheres. https://arxiv.org/abs/1309.5755

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