Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity of solutions for a class of fractional
  $p(x,\cdot)$-Kirchhoff type problems without the Ambrosetti-Rabinowitz
  condition   We are interested in the existence of solutions for the following fractional
$p(x,\cdot)$-Kirchhoff type problem $$ \left\{\begin{array}{ll} M \,
\left(\displaystyle\int_{\Omega\times \Omega} \
\displaystyle{\frac{|u(x)-u(y)|^{p(x,y)}}{p(x,y) \ |x-y|^{N+p(x,y)s}}} \ dx \,
dy\right)(-\Delta)^{s}_{p(x,\cdot)}u = f(x,u), \quad x\in \Omega, \\ \\ u= 0,
\quad x\in \partial\Omega, \end{array}\right.$$ where
$\Omega\subset\mathbb{R}^{N}$, $N\geq 2$ is a bounded smooth domain,
$s\in(0,1),$ $p: \overline{\Omega}\times \overline{\Omega} \rightarrow (1,
\infty)$, $(-\Delta)^{s}_{p(x,\cdot)}$ denotes the $p(x,\cdot)$-fractional
Laplace operator, $M: [0,\infty) \to [0, \infty),$ and $f: \Omega \times
\mathbb{R} \to \mathbb{R}$ are continuous functions. Using variational methods,
especially the symmetric mountain pass theorem due to Bartolo-Benci-Fortunato
(Nonlinear Anal. 7:9 (1983), 981-1012), we establish the existence of
infinitely many solutions for this problem without assuming the
Ambrosetti-Rabinowitz condition. Our main result in several directions extends
previous ones which have recently appeared in the literature.

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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
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The categories of this paper are: nlin
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: econ