Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and concentration of positive solutions for nonlinear
  Kirchhoff type problems with a general critical nonlinearity   We are concerned with the following Kirchhoff type equation $$-\varepsilon^2
M \left(\varepsilon^{2-N} \int_{\mathbb{R}^N} | \nabla u|^2\, \mathrm{d}
x\right) \Delta u+V(x)u = f(u),\ x \in \mathbb{R}^N,\ \ N\ge2, $$ where $M \in
C(\mathbb{R}^+,\mathbb{R}^+)$, $V\in C(\mathbb{R}^N,\mathbb{R}^+)$ and $f(s)$
is of critical growth. In this paper, we construct a localized bound state
solution concentrating at a local minimum of $V$ as $\varepsilon\to 0$ under
certain conditions on $f(s)$, $M$ and $V$. In particular, the monotonicity of
$f(s)/s$ and the Ambrosetti-Rabinowitz condition are not required.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci