Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence, uniqueness and global behavior of the solutions to some
  nonlinear vector equations in a finite dimensional Hilbert space   The initial value problem and global properties of solutions are studied for
the vector equation: $\Big(\|u'\|^{l}u'\Big)'+\|A^{\frac{1}{2}}u\|^\beta
Au+g(u')=0$ in a finite dimensional Hilbert space under suitable assumptions on
$g$.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex