Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An energy constrained method for the existence of layered type solutions
  of NLS equations   We study the existence of positive solutions on $\R^{N+1}$ to semilinear
elliptic equation $-\Delta u+u=f(u)$ where $N\geq 1$ and $f$ is modeled on the
power case $f(u)=|u|^{p-1}u$. Denoting with $c$ the mountain pass level of
$\f(u)=\tfrac 12\|u\|^{2}_{H^{1}(\R^{N})}-\int_{\R^{N}}F(u)\, dx$, $u\in
H^{1}(\R^{N})$ ($F(s)=\int_{0}^{s}f(t)\, dt$), we show, via a new energy
constrained variational argument, that for any $b\in [0,c)$ there exists a
positive bounded solution $v_{b}\in C^{2}(\R^{N+1})$ such that
$E_{v_{b}}(y)=\tfrac
12\|\partial_{y}v_{b}(\cdot,y)\|^{2}_{L^{2}(\R^{N})}-V(v_{b}(\cdot,y))=-b$ and
$v(x,y)\to 0$ as $|x|\to+\infty$ uniformly with respect to $y\in\R$. We also
characterize the monotonicity, symmetry and periodicity properties of $v_{b}$.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex