Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularly perturbed fractional Schr\"{o}dinger equation involving a
  general critical nonlinearity   In this paper, we are concerned with the existence and concentration
phenomena of solutions for the following singularly perturbed fractional
Schr\"{o}dinger problem \begin{align*} \varepsilon^{2s}(-\Delta)^su+V(x)u=f(u)
\ \ \ \mbox{in} \ \ \ \mathbb{R}^N, \end{align*} where $N>2s$ and the
nonlinearity $f$ has critical growth. By using the variational approach, we
construct a localized bound-state solution concentrating around an isolated
component of the positive minimum point of $V$ as $\varepsilon\rightarrow 0$.
Our result improves the study made in X. He and W. Zou ({\it Calc. Var. Partial
Differential Equations}. 55-91(2016)), in the sense that, in the present paper,
the {\it Ambrosetti-Rabinowitz} condition and {\it monotonicity} condition on
$f(t)/t$ are not required.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org