Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary value problem with fractional p-Laplacian operator   The aim of this paper is to obtain the existence of solution for the
fractional p-Laplacian Dirichlet problem with mixed derivatives
\begin{eqnarray*}
&{_{t}}D_{T}^{\alpha}\left(|_{0}D_{t}^{\alpha}u(t))|^{p-2}{_{0}}D_{t}^{\alpha}u(t)\right)
= f(t,u(t)), \;t\in [0,T],\\ &u(0) = u(T) = 0, \end{eqnarray*} where
$\frac{1}{p} < \alpha <1$, $1<p<\infty$ and $f:[0,T]\times \mathbb{R} \to
\mathbb{R}$ is a Carath\'eodory function wich satisfies some growth conditions.
We obtain the existence of nontrivial solution by using the Mountain Pass
Theorem.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int