Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and asymptotic behavior of nontrivial solutions to the
  Swift-Hohenberg equation   In this paper, we discuss several results regarding existence, non-existence
and asymptotic properties of solutions to $u""+qu"+f(u)=0$, under various
hypotheses on the parameter $q$ and on the potential $F(t)=\int_0^tf(s)\, ds$,
generally assumed to be bounded from below. We prove a non-existence result in
the case $q\le 0$ and an existence result of periodic solution for: 1) almost
every suitably small (depending on $F$), positive values of $q$; 2) all
suitably large (depending on $F$) values of $q$. Finally, we describe some
conditions on $F$ which ensure that some (or all) solutions $u_q$ to the
equation satisfy $\|u_q\|_\infty\to 0$, as $q\downarrow 0$.

5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat