Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of positive solutions to biharmonic equations on Heisenberg
  group   In this note, we establish the existence of a positive solution and its
stability to the following problem
$$\Delta_{\mathbb{H}^n}^2u=a(\xi)u-f(\xi,u)\text{ in }\Omega, \,\,\,
u|_{\partial\Omega} = 0 =\left.\Delta_{\mathbb{H}^n} u|_{\partial\Omega},$$ on
Heisenberg group.

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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci