Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalent conditions for existence of three solutions for a problem
  with discontinuous and strongly-singular terms   In this paper, we are concerned with a Kirchhoff problem in the presence of a
strongly-singular term perturbed by a discontinuous nonlinearity of the
Heaviside type in the setting of Orlicz-Sobolev space. The presence of both
strongly-singular and non-continuous terms bring up difficulties in associating
a differentiable functional to the problem with finite energy in the whole
space $W_0^{1,\Phi}(\Omega)$. To overcome this obstacle, we established an
optimal condition for the existence of $W_0^{1,\Phi}(\Omega)$-solutions to a
strongly-singular problem, which allows us to constrain the energy functional
to a subset of $W_0^{1,\Phi}(\Omega)$ to apply techniques of convex analysis
and generalized gradient in Clarke sense.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn