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• W2067069245 abstract "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 $p int_{Omega}abs{nabla u_p}^2to 16pi equadhbox{as}prightarrow+inftyqquad (*)$ and we are interested in the shape and the asymptotic behavior as $prightarrow+infty$. 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 $p$." @default.
• W2067069245 created "2016-06-24" @default.
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• W2067069245 date "2013-02-01" @default.
• W2067069245 modified "2023-10-11" @default.
• W2067069245 title "Lane–Emden problems: Asymptotic behavior of low energy nodal solutions" @default.
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• W2067069245 doi "https://doi.org/10.1016/j.anihpc.2012.06.005" @default.
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