Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic solutions of wave equations for asymptotically full measure
  sets of frequencies   We prove existence and multiplicity of small amplitude periodic solutions of
the completely resonant wave equation u_tt - u_xx + f(x,u)=0 with Dirichlet
boundary conditions where f(x,u)=a_2 u^2 + a_3(x) u^3 + O(u^4) or f(x,u)= a_4
u^4 + O(u^5) for a Cantor-like set of frequencies omega of asymptotically full
measure at omega=1.

19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ