Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A global branch approach to normalized solutions for the Schr\"odinger
  equation   We present a novel approach to study the existence, non-existence and
multiplicity of prescribed mass positive solutions to a Schr\"odinger equation
of the form \begin{equation*} -\Delta u+\lambda u=g(u), \quad u \in
H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} This approach permits to handle
in a unified way nonlinearities $g(s)$ which are either mass subcritical, mass
critical or mass supercritical. Among its main ingredients is the study of the
asymptotic behaviors of the positive solutions as $\lambda\rightarrow 0^+$ or
$\lambda\rightarrow +\infty$ and the existence of an unbounded continuum of
solutions in $(0, + \infty) \times H^1(\mathbb{R}^N)$

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex