Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hard Implicit Function Theorem via the DSM   Sufficient conditions are given for a hard implicit function theorem to hold.
The result is established by an application of the Dynamical Systems Method
(DSM). It allows one to solve a class of nonlinear operator equations in the
case when the Fr\'echet derivative of the nonlinear operator is a smoothing
operator, so that its inverse is an unbounded operator.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: econ
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci