Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive solutions of indefinite semipositone problems via sub-super
  solutions   Let $\Omega\subset\mathbb{R}^{N}$, $N\geq1$, be a smooth bounded domain, and
let $m:\Omega\rightarrow\mathbb{R}$ be a possibly sign-changing function. We
investigate the existence of positive solutions for the semipositone problem
$-\Delta u=\lambda m(x)(f(u)-k)$ in $\Omega$, $u=0$ on $\partial\Omega$, where
$\lambda,k>0$ and $f$ is either sublinear at infinity with $f(0)=0$, or $f$ has
a singularity at $0$. We prove the existence of a positive solution for certain
ranges of $\lambda$ provided that the negative part of $m$ is suitably small.
Our main tool is the sub-supersolutions method, combined with some rescaling
properties.

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph