Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entire large solutions for semilinear elliptic equations   We analyze the semilinear elliptic equation $\Delta u=\rho(x) f(u)$, $u>0$ in
${\mathbf R}^D$ $(D\ge3)$, with a particular emphasis put on the qualitative
study of entire large solutions, that is, solutions $u$ such that
$\lim_{|x|\rightarrow +\infty}u(x)=+\infty$. Assuming that $f$ satisfies the
Keller-Osserman growth assumption and that $\rho$ decays at infinity in a
suitable sense, we prove the existence of entire large solutions. We then
discuss the more delicate questions of asymptotic behavior at infinity,
uniqueness and symmetry of solutions.

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The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an