Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the solutions of a singular elliptic equation concentrating on two
  orthogonal spheres   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.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: math-ph