Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sharp stability criterion for single well Duffing and Duffing-like
  equations   We refine some previous sufficient conditions for exponential stability of
the linear ODE $$ u''+ cu' + (b+a(t))u = 0$$ where $b, c>0$ and $a$ is a
bounded nonnegative time dependent coefficient. This allows to improve some
results on uniqueness and asymptotic stability of periodic or almost periodic
solutions of the equation$$ u''+ cu' + g(u)=f(t) $$where $c>0$, $f \in L^\infty
(R)$ and $g\in C^1(R)$ satisfies some sign hypotheses. The typical case is $
g(u) = bu + a\vert u\vert^p u $ with $a\ge 0 , b>0.$ Similar properties are
valid for evolution equations of the form $$ u''+ cu' + (B+A(t))u = 0$$ where
$A(t) $ and $B$ are self-adjoint operators on a real Hilbert space $H$ with $B$
coercive and $A(t)$ bounded in $L(H)$ with a sufficiently small bound of its
norm in $L^{\infty}(R+, L(H))$ .

9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph