Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonradial blow-up solutions of sublinear elliptic equations with
  gradient term   Let $f$ be a continuous and non-decreasing function such that $f>0$ on
$(0,\infty)$, $f(0)=0$, $\sup \_{s\geq 1}f(s)/s< \infty$ and let $p$ be a
non-negative continuous function. We study the existence and nonexistence of
explosive solutions to the equation $\Delta u+|\nabla u|=p(x)f(u)$ in $\Omega,$
where $\Omega$ is either a smooth bounded domain or $\Omega=\RR^N$. If $\Omega$
is bounded we prove that the above problem has never a blow-up boundary
solution. Since $f$ does not satisfy the Keller-Osserman growth condition at
infinity, we supply in the case $\Omega=\RR^N$ a necessary and sufficient
condition for the existence of a positive solution that blows up at infinity.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th