Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite Morse index solutions to the quadharmonic Lane-Emden equation   In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic
Lane-Emden equation, derive a monotonicity formula and classify the finite
Morse index solution to the following quadharmonic Lane-Emden equation:
\noindent \begin{equation}\nonumber \Delta^4
u=|u|^{p-1}u\;\;\;\;\hbox{in}\;\;\;\;\; \R^n. \end{equation} As a byproduct, we
also get a monotonicity formula for the quadharmonic maps $ \Delta^4 u=0$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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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: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas