Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlocal Pertubations of Fractional Choquard Equation   We study the equation \begin{equation} (-\Delta)^{s}u+V(x)u=
(I_{\alpha}*|u|^{p})|u|^{p-2}u+\lambda(I_{\beta}*|u|^{q})|u|^{q-2}u \quad\mbox{
in } \R^{N}, \end{equation} where $I_\gamma(x)=|x|^{-\gamma}$ for any
$\gamma\in (0,N)$, $p, q >0$, $\alpha,\beta\in (0,N)$, $N\geq 3$ and $ \lambda
\in R$. First, the existence of a groundstate solutions using minimization
method on the associated Nehari manifold is obtained. Next, the existence of
least energy sign-changing solutions is investigated by considering the Nehari
nodal set.

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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat