Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity and concentration behavior of positive solutions for a
  Schrodinger-Kirchhoff type problem via penalization method   In this paper we are concerned with questions of multiplicity and
concentration behavior of positive solutions of the elliptic problem
$$\left\{\begin{array}{rcl} \mathcal{L}_{\varepsilon}u = f(u) \ \ \mbox{in} \ \
\mathbb{R}^3,\\ u>0 \ \ \mbox{in} \ \ \mathbb{R}^3,\\ u \in H^1 (\mathbb{R}^3),
\end{array} \right.$$ where $\varepsilon$ is a small positive parameter,
$f:\mathbb{R}\rightarrow \mathbb{R}$ is a continuous function,
$\mathcal{L}_{\varepsilon}$ is a nonlocal operator defined by $$
\mathcal{L}_{\varepsilon} u = M \left(\frac{1}{\varepsilon} \int_{\mathbb{R}^3}
|\nabla u|^2 + \frac{1}{\varepsilon^3} \int_{\mathbb{R}^3} V(x) u^{2}\right)
\left[-\varepsilon^2\Delta u + V(x)u \right],$$ $M:\mathbb{R}_+\to
\mathbb{R}_+$ and $V:\mathbb{R}^3 \to \mathbb{R}$ are continuous functions
which verify some hypotheses.

37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas