Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ekeland's inverse function theorem in graded Fr\'echet spaces revisited
  for multifunctions   In this paper, we present some implicit function theorems for set-valued
mappings between Fr\'echet spaces. The proof relies on Lebesgue's Dominated
Convergence Theorem and on Ekeland's variational principle. An application to
the existence of solutions of differential equations in Fr\'echet spaces with
non-smooth data is given.

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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: physics