Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-existence of nonnegative separate variable solutions to a porous
  medium equation with spatially dependent nonlinear source   The non-existence of nonnegative compactly supported classical solutions to
$$- \Delta V(x) - |x|^\sigma V(x) + \frac{V^{1/m}(x)}{m-1} = 0, \qquad
x\in\mathbb{R}^N,$$ with $m>1$, $\sigma>0$, and $N\ge 1$, is proven for
$\sigma$ sufficiently large. More precisely, in dimension $N\geq4$, the optimal
lower bound on $\sigma$ for non-existence is identified, namely
$$\sigma\geq\sigma_c := \frac{2(m-1)(N-1)}{3m+1},$$ while, in dimensions
$N\in\{1,2,3\}$, the lower bound derived on $\sigma$ improves previous ones
already established in the literature. A by-product of this result is the
non-existence of nonnegative compactly supported separate variable solutions to
a porous equation medium equation with spatially dependent superlinear source.

1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph