Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-trivial solutions of local and non-local Neumann boundary-value
  problems   We prove new results on the existence, non-existence, localization and
multiplicity of nontrivial solutions for perturbed Hammerstein integral
equations. Our approach is topological and relies on the classical fixed point
index. Some of the criteria involve a comparison with the spectral radius of
some related linear operators. We apply our results to some boundary value
problems with local and nonlocal boundary conditions of Neumann type. We
illustrate in some examples the methodologies used.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org