Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nonlinear boundary value problem corresponding to $N$-dimensional
  inverse spectral problem   We establish a relationship between an inverse optimization spectral problem
for N-dimensional Schr\"odinger equation $ -\Delta \psi+q\psi=\lambda \psi $
and a solution of the nonlinear boundary value problem $-\Delta u+q_0 u=\lambda
u- u^{\gamma-1},~~u>0,~~
  u|_{\partial \Omega}=0$. Using this relationship, we find an exact solution
for the inverse optimization spectral problem, investigate its stability and
obtain new results on the existence and uniqueness of the solution for the
nonlinear boundary value problem.

24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th