Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and qualitative properties of radial solutions of the
  Lane-Emden-Fowler equation on Riemannian models   We study existence, uniqueness and stability of radial solutions of the
Lane-Emden-Fowler equation $-\Delta_g u=|u|^{p-1}u$ in a class of Riemannian
models $(M,g)$ of dimension $n\ge 3$ which includes the classical hyperbolic
space $\mathbb H^n$ as well as manifolds with sectional curvatures unbounded
below. Sign properties and asymptotic behavior of solutions are influenced by
the critical Sobolev exponent while the so-called Joseph-Lundgren exponent is
involved in the stability of solutions.

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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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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: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph