Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville type theorems and periodic solutions for $\chi^{(2)}$ type
  systems with non-homogeneous nonlinearities   In the present paper we derive Liouville type results and existence of
periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous
nonlinearities. Moreover, we prove both universal bounds as well as singularity
and decay estimates for this class of problems. In this study, we have to face
new difficulties due to the non-homogenous nonlinearities. To overcome this
issue, we carry out delicate integral estimates for this class of
nonlinearities and modify the usual scaling and blow up arguments. This seems
to be the first result for parabolic systems with non-homogeneous
nonlinearities.

27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom