Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational properties of the first curve of the Fu\v{c}\'{\i}k spectrum
  for elliptic operators   In this paper we present a new variational characteriztion of the first
nontrival curve of the Fu\v{c}\'{\i}k spectrum for elliptic operators with
Dirichlet boundary conditions. Moreover, we describe the asymptotic behaviour
and some properties of this curve and of the corresponding eigenfunctions. In
particular, this new characterization allows us to compare the first curve of
the Fu\v{c}\'{\i}k spectrum with the infinitely many curves we obtained in
previous works (see R. Molle, D. Passaseo, New properties of the Fu\v{c}\'{\i}k
spectrum. C. R. Math. Acad. Sci. Paris 351 (2013), no. 17/18, 681--685 and R.
Molle, D. Passaseo, Infinitely many new curves of the Fu\v{c}\'{\i}k spectrum.
Ann. I. H. Poincar\'e - AN (2014),
http://dx.doi.org/10.1016/j.anihpc.2014.05.007): for example, we show that
these curves are all asymptotic to the same lines as the first curve, but they
are all distinct from such a curve.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom