Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform a priori estimates for positive solutions of higher order
  Lane-Emden equations in $\mathbb{R}^n$   In this paper, we study the existence of uniform a priori estimates for
positive solutions to Navier problems of higher order Lane-Emden equations
\begin{equation*}
  (-\Delta)^{m}u(x)=u^{p}(x), \qquad \,\, x\in\Omega \end{equation*} for all
large exponents $p$, where $\Omega\subset\mathbb{R}^{n}$ is a star-shaped or
strictly convex bounded domain with $C^{2m-2}$ boundary, $n\geq4$ and $2\leq
m\leq\frac{n}{2}$. Our results extend those of previous authors for second
order $m=1$ to general higher order cases $m\geq2$.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph