Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymmetric variations of multifunctions with application to functional
  inclusions   Under certain initial conditions, we prove the existence of set-valued
selectors of univariate compact-valued multifunctions of bounded (Jordan)
variation when the notion of variation is defined taking into account only the
Pompeiu asymmetric excess between compact sets from the target metric space.
For this, we study subtle properties of the directional variations. We show by
examples that all assumptions in the main existence result are essential. As an
application, we establish the existence of set-valued solutions $X(t)$ of
bounded variation to the functional inclusion of the form $X(t)\subset
F(t,X(t))$ satisfying the initial condition $X(t_0)=X_0$.

13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas