Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple solutions for superlinear fractional problems via theorems of
  mixed type   In this paper we investigate the existence of multiple solutions for the
following two fractional problems \begin{equation*} \left\{\begin{array}{ll}
(-\Delta_{\Omega})^{s} u-\lambda u= f(x, u) &\mbox{in} \Omega \\ u=0 &\mbox{in}
\partial \Omega \end{array} \right. \end{equation*} and \begin{equation*}
\left\{\begin{array}{ll} (-\Delta_{\mathbb{R}^{N}})^{s} u-\lambda u= f(x, u)
&\mbox{in} \Omega \\ u=0 &\mbox{in} \mathbb{R}^{N}\setminus \Omega, \end{array}
\right. \end{equation*} where $s\in (0,1)$, $N>2s$, $\Omega$ is a smooth
bounded domain of $\mathbb{R}^{N}$, and $f:\bar{\Omega}\times
\mathbb{R}\rightarrow \mathbb{R}$ is a superlinear continuous function which
does not satisfy the well-known Ambrosetti-Rabinowitz condition. Here
$(-\Delta_{\Omega})^{s}$ is the spectral Laplacian and
$(-\Delta_{\mathbb{R}^{N}})^{s}$ is the fractional Laplacian in
$\mathbb{R}^{N}$. By applying variational theorems of mixed type due to Marino
and Saccon and Linking Theorem, we prove the existence of multiple solutions
for the above problems.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph