Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On weak solutions to first-order discount mean field games   In this paper, we establish the existence and uniqueness of weak solutions to
first-order discount mean field games and a stability result to give the
existence for the ergodic problem. We show an example to illustrate the
multiplicity of weak solutions to the ergodic problem. With this motivation, we
address a selection condition, which is a necessary condition that any limit of
solutions under subsequence satisfies. As an application, we show a nontrivial
example to get the convergence of weak solutions.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom