Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic Solutions of Generalized Schr\"odinger Equations on Cayley
  Trees   In this paper we define a discrete generalized Laplacian with arbitrary real
power on a Cayley tree. This Laplacian is used to define a discrete generalized
Schr\"odinger operator on the tree. The case discrete fractional Schr\"odinger
operators with index $0 < \alpha < 2$ is considered in detail, and periodic
solutions of the corresponding fractional Schr\"odinger equations are
described. This periodicity depends on a subgroup of a group representation of
the Cayley tree. For any subgroup of finite index we give a criterion for
eigenvalues of the Schr\"odinger operator under which periodic solutions exist.
For a normal subgroup of infinite index we describe a wide class of periodic
solutions.

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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: econ