Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of positive periodic solutions with some peaks   This work deals with the semi linear equation $-\Delta u+u-u^p=0$ in $\R^N$,
$2\leq p<{N+2\over N-2}$. We consider the positive solutions which are
${2\pi\over\ep}$-periodic in $x_1$ and decreasing to 0 in the other variables,
uniformly in $x_1$. Let a periodic configuration of points be given on the
$x_1$-axis, which repel each other as the period tends to infinity. If there
exists a solution which has these points as peaks, we prove that the points
must be asymptotically uniformly distributed on the $x_1$-axis. Then, for $\ep$
small enough, we prove the uniqueness up to a translation of the positive
solution with some peaks on the $x_1$-axis, for a given minimal period in
$x_1$.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: physics