Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An application of a theorem of G. Zwirner to a class of non-linear
  elliptic systems in divergence form   A theorem on the solutions of the problem $U'(w)=\gamma F(U(w),w),\
U(w_1)=u_2,\ U(w_2)=u_2$ is applied for finding the functional solutions of the
system of partial differential equations
  \begin{equation} \nabla\cdot(a(u,w)\nabla u)=0,\ u=u_1\ on \Gamma_1,\ u=u_2\
on \Gamma_2,\ \frac{\partial u}{\partial n}=0\ on\ \Gamma_3 \end{equation}
  \begin{equation} \nabla\cdot(b(u,w)\nabla w)=0, \ w=w_1\ on \Gamma_1,\ w=w_2\
on\ \Gamma_2,\ \frac{\partial u}{\partial n}=0\ on\ \Gamma_3. \end{equation}
The problem of existence and uniqueness of solutions is also considered.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th