Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weights sharing the same eigenvalue   Here is the simplest particular case of our main result: let $f:{\bf R}\to
{\bf R}$ be a function of class $C^1$, with $\sup_{\bf R}f'>0$, such that
$$\lim_{|\xi|\to +\infty}{{f(\xi)}\over {\xi}}=0\ .$$ Then, for each
$\lambda>{{\pi^2}\over {\sup_{\bf R}f'}}$, the set of all $u\in H^1_0(]0,1[)$
for which the problem $$\cases{-v''=\lambda f'(u(x)) v & in $]0,1[$\cr & \cr
v(0)=v(1)=0\cr}$$ has a non-zero solution is closed and not $\sigma$-compact in
$H^1_0(]0,1[)$.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph