Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness and sign properties of minimizers in a quasilinear indefinite
  problem   Let $1<q<p$ and $a\in C(\overline{\Omega})$ be sign-changing, where $\Omega$
is a bounded and smooth domain of $\mathbb{R}^{N}$. We show that the functional
\[ I_{q}(u):=\int_{\Omega}\left( \frac{1}{p}|\nabla
u|^{p}-\frac{1}{q}a(x)|u|^{q}\right) , \] has exactly one nonnegative minimizer
$U_{q}$ (in $W_{0}^{1,p}(\Omega)$ or $W^{1,p}(\Omega)$). In addition, we prove
that $U_{q}$ is the only possible \textit{positive} solution of the associated
Euler-Lagrange equation, which shows that this equation has at most one
positive solution. Furthermore, we show that if $q$ is close enough to $p$ then
$U_{q}$ is positive, which also guarantees that minimizers of $I_{q}$ do not
change sign. Several of these results are new even for $p=2$.

19
The categories of this paper are: eess
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an