Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz perturbations of differentiable implicit functions   Let $y=f(x)$ be a continuously differentiable implicit function solving the
equation $F(x,y)=0$ with continuously differentiable $F.$ In this paper we show
that if $F_\eps$ is a Lipschitz function such that the Lipschitz constant of
$F_\eps-F$ goes to 0 as $\eps\to 0$ then the equation $F_\eps(x,y)=0$ has a
Lipschitz solution $y=f_\eps(x)$ such that the Lipschitz constant of $f_\eps-f$
goes to 0 as $\eps\to 0$ either. As an application we evaluate the length of
time intervals where the right hand parts of some nonautonomous discontinuous
systems of ODEs are continuously differentiable with respect to state
variables. The latter is done as a preparatory step toward generalizing the
second Bogolyubov's theorem for discontinuous systems.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg