Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville type theorems for stable solutions of the weighted elliptic
  system   We examine the weighted elliptic system \begin{equation*} \begin{cases}
-\Delta u=(1+|x|^2)^{\frac{\alpha}{2}} v,\\ -\Delta
v=(1+|x|^2)^{\frac{\alpha}{2}} u^p, \end{cases} \quad \mbox{in}\;\
\mathbb{R}^N, \end{equation*}where $N \ge 5$, $p>1$ and $\alpha >0$. We prove
Liouville type results for the classical positive (nonnegative) stable
solutions in dimension $N<\ell+\dfrac{\alpha (\ell-2)}{2}$ ($N
<\ell+\dfrac{\alpha (\ell-2)(p+3)}{4(p+1)}$) and $\ell \ge 5$, $p \in
(1,p_*(\ell))$. In particular, for any $p>1$ and $\alpha > 0$, we obtain the
nonexistence of classical positive (nonnegative) stable solutions for any $N
\le 12+5 \alpha$ ($N\le 12+\dfrac{5\alpha (p+3)}{2(p+1)}$).

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc