Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lane Emden problems: asymptotic behavior of low energy nodal solutions   We study the nodal solutions of the Lane Emden Dirichlet problem $-\Delta u =
|u|^{p-1}u with DBC on a smooth bounded domain $\Omega$ in $\IR^2$ and where
$p>1$. We consider solutions $u_p$ satisfying $p \int_{\Omega}\abs{\nabla
u_p}^2\to 16\pi e\quad\hbox{as}p\rightarrow+\infty\qquad (*)$ and we are
interested in the shape and the asymptotic behavior as $p\rightarrow+\infty$.
First we prove that (*) holds for least energy nodal solutions. Then we obtain
some estimates and the asymptotic profile of this kind of solutions. Finally,
in some cases, we prove that $pu_p$ can be characterized as the difference of
two Green's functions and the nodal line intersects the boundary of $\Omega$,
for large $p$.

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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: econ