Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions to a nonlinear Schr\"odinger equation with periodic potential
  and zero on the boundary of the spectrum   We study the following nonlinear Schr\"odinger equation $$-\Delta u + V(x) u
= g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right
boundary point of the essential spectrum of $-\Delta+V$. The superlinear and
subcritical term g satisfies a Nehari type monotonicity condition. We employ a
Nehari manifold type technique in a strongly indefitnite setting and obtain the
existence of a ground state solution. Moreover we get infinitely many
geometrically distinct solutions provided that g is odd.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn