Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear nonlocal problem for the abstract time-dependent non-homogeneous
  Schr\"odinger equation   A nonlocal-in-time problem for the abstract Schr\"odinger equation is
considered. By exploiting the linear nature of nonlocal condition we derive an
exact representation of the solution operator under assumptions that the
spectrum of Hamiltonian is contained in the horizontal strip of complex plane.
The derived representation permits us to establish the necessary and sufficient
conditions for the problem's well-posedness and the existence of its mild,
strong solutions. Furthermore, we present new sufficient conditions for the
existence of solution which extend the available results to the case when some
nonlocal parameters are unbounded. Two examples are provided.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom