Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual morse index estimates and application to Hamiltonian systems with
  P-boundary conditions   In this paper, we study the multiplicity of Hamiltonian systems with
P-boundary conditions.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci