Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Sturm Oscillation: from the interval to a star   The Sturm oscillation property, i.e. that the $n$-th eigenfunction of a
Sturm-Liouville operator on an interval has $n -1$ zeros (nodes), has been well
studied. This result is known to hold when the interval is replaced by a metric
(quantum) tree graph. We prove that the solutions of the real stationary
nonlinear Schr\"odinger equation on an interval satisfy a nonlinear version of
the Sturm oscillation property. However, we show that unlike the linear theory,
the nonlinear version of the Sturm oscillation breaks down already for a star
graph. We point out conditions under which this violation can be assured.

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The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
16
The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th