Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Levinson Theorem for Differential Equations with Piecewise Constant
  Argument Generalized   In this work, it is presented an adaptation of an asymptotic theorem of N.
Levinson of 1948, to differential equation with piecewise constant argument
generalized, which were introduced by M. Akhmet in 2007. By simplicity and
without loss of generality, the case where the argument is delayed is
considered. The N. Levinson's theorem which is adapted is that dealt by M. S.
P. Eastham in his work which is present in this bibliography. The more relevant
hypotheses of this theorem are highlighted an it is established a version of
this theorem with these hypotheses for ordinary differential equations. Such a
version is that which is adapted to differential equation with piecewise
constant argument generalized. The adaptation is proved by mean the Banach
fixed point where contractive operator is built form a suitable version of the
constant variation formula.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th