Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation results of critical elliptic equations of
  Caffarelli-Kohn-Nirenberg type   We find for small $\epsilon$ positive solutions to the equation
\[-\textrm{div} (|x|^{-2a}\nabla u)-\displaystyle{\frac{\lambda}{|x|^{2(1+a)}}}
u= \Big(1+\epsilon k(x)\Big)\frac{u^{p-1}}{|x|^{bp}}\] in ${\mathbb{R}}^N$,
which branch off from the manifold of minimizers in the class of radial
functions of the corresponding Caffarelli-Kohn-Nirenberg type inequality.
Moreover, our analysis highlights the symmetry-breaking phenomenon in these
inequalities, namely the existence of non-radial minimizers.

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The categories of this paper are: nlin
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int