Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of eigenvalues of the zero-range perturbation of the
  discrete bilaplacian   We consider the family $$ \hat {\bf h}_\mu:=\hat\varDelta\hat \varDelta - \mu
\hat {\bf v},\qquad\mu\in\mathbb{R}, $$ of discrete Schr\"odinger-type
operators in one-dimensional lattice $\mathbb{Z}$, where $\hat \varDelta$ is
the discrete Laplacian and $\hat{\bf v}$ is of zero-range. We prove that for
any $\mu\ne0$ the discrete spectrum of $\hat {\bf h}_\mu$ is a singleton
$\{e(\mu)\},$ and $e(\mu)<0$ for $\mu>0$ and $e(\mu)>4$ for $\mu<0.$ Moreover,
we study the properties of $e(\mu)$ as a function of $\mu,$ in particular, we
find the asymptotics of $e(\mu)$ as $\mu\searrow0$ and $\mu\nearrow0.$

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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin