Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalized solutions to the mixed dispersion nonlinear Schr\"odinger
  equation in the mass critical and supercritical regime   In this paper, we study the existence of solutions to the mixed dispersion
nonlinear Schr\"odinger equation $$ \gamma \Delta ^2 u -\Delta u + \alpha
u=|u|^{2 \sigma} u, \quad u \in H^2(\R^N), $$ under the constraint $$
\int_{\R^N}|u|^2 \, dx =c>0. $$ We assume $\gamma >0, N \geq 1, 4 \leq \sigma N
< \frac{4N}{(N-4)^+}$, whereas the parameter $\alpha \in \R$ will appear as a
Lagrange multiplier. Given $c \in \R^+$, we consider several questions
including the existence of ground states, of positive solutions and the
multiplicity of radial solutions. We also discuss the stability of the standing
waves of the associated dispersive equation.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph