Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonexistence of positive solutions for Henon equation   We consider the semilinear elliptic equation $$ -\Delta u = |x|^\alpha u^p
\quad \hbox{in } \mathbb{R}^N, $$ where $N\ge 3$, $\alpha>-2$ and $p>1$. We
show that there are no positive solutions provided that the exponent $p$
additionally verifies $$ 1<p<\frac{N+2\alpha+2}{N-2}. $$ This solves an open
problem posed in previous literature, where only the radially symmetric case
was fully understood. We also characterize all positive solutions when
$p=\frac{N+2\alpha+2}{N-2}$ and $-2<\alpha<0$.

12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol