Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on radial solutions of $\Delta^2 u + u^{-q} = 0$ in $\mathbb R^3$
  with exactly quadratic growth at infinity   Of interest in this note is the following geometric interesting equation
$\Delta^2 u + u^{-q} = 0$ in $\mathbb R^3$. It was found by Choi-Xu (J.
Differential Equations 246, 216-234) and McKenna-Reichel (Electron. J.
Differential Equations 37 (2003)) that the condition $q>1$ is necessary and any
radially symmetric solution grows at least linearly and at most quadratically
at infinity for any $q>1$. In addition, when $q>3$ any radially symmetric
solution is either exactly linear growth or exactly quadratic growth at
infinity. Recently, Guerra (J. Differential Equations 253, 3147-3157) has shown
that the equation always admits a unique radially symmetric solution of exactly
given linear growth at infinity for any $q>3$ which is also necessary. In this
note, by using the phase-space analysis, we show the existence of infinitely
many radially symmetric solutions of exactly given quadratic growth at infinity
for any $q>1$.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org