Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of solutions to higher order Lane-Emden type systems   We prove existence results for the Lane-Emden type system
  \[ \begin{cases}
  \begin{aligned}
  (-\Delta)^{\alpha} u=\left| v \right|^q \\
  (-\Delta)^{\beta} v= \left| u \right|^p
  \end{aligned} \text{ in } B_1 \subset \mathbb{R}^N \\
  \frac{\partial^{r} u}{\partial \nu^{r}}=0, \, r=0, \dots, \alpha-1, \text{ on
} \partial B_1 \\
  \frac{\partial^{r} v}{\partial \nu^{r}}=0, \, r=0, \dots, \beta-1, \text{ on
} \partial B_1.
  \end{cases}
  \]
  where $B_1$ is the unitary ball in $\mathbb{R}^N$, $N >\max \{2\alpha, 2\beta
\}$, $\nu$ is the outward pointing normal, $\alpha, \beta \in \mathbb{N}$,
$\alpha, \beta \ge 1$ and $(-\Delta)^{\alpha}= -\Delta((-\Delta)^{\alpha-1})$
is the polyharmonic operator. A continuation method together with a priori
estimates will be exploited. Moreover, we prove uniqueness for the particular
case $\alpha=2$, $\beta=1$ and $p, q>1$.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th