Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting function of magnetic eigenvalues for non-definite sign
  perturbations   We consider the perturbed operator $H(b,V) := H(b,0) + V$, where $H(b,0)$ is
the $3$d Hamiltonian of Pauli with non-constant magnetic field, and $V$ is
\textit{a non-definite sign electric potential} decaying exponentially with
respect to the variable along the magnetic field. We prove that the only
resonances of $H(b,V)$ near the low ground energy zero of $H(b,0)$ are its
eigenvalues and are concentrated in the semi axis $(-\infty,0)$. Further, we
establish new asymptotic expansions, upper and lower bounds on their number
near zero.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys