Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity of negative-energy solutions for singular-superlinear
  Schr\"odinger equations with indefinite-sign potential   We are concerned with the multiplicity of positive solutions for the singular
superlinear and subcritical Schr\"odinger equation
  $$
  \begin{array}{c}
  -\Delta u +V(x)u=\lambda a(x)u^{-\gamma}+b(x)u^{p}~\mbox{in}~ \mathbb{R}^{N},
  \end{array}
  $$
  beyond the Nehari extremal value, as defined in Il'yasov [Topol. Methods
Nonlinear Anal., 2017], when the potential $b \in L^{\infty}(\mathbb{R}^{N})$
may change its sign, $0<a\in L^{\frac{2}{1+\gamma}}(\mathbb{R}^{N})$, $V$ is a
positive continuous function, $N\geq 3$ and $\lambda>0$ is a real parameter.
The main difficulties come from the non-differentiability of the energy
functional and the fact that the intersection of the boundaries of the
connected components of the Nehari set is non empty. We overcome these
difficulties by exploring topological structures of that boundary to build
non-empty sets whose boundaries have empty intersection and minimizing over
them by controlling the energy level.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin