We consider the semilinear Lane-Emden problem (Ep) -Delta u = |u|^{p−1} u in Omega; u = 0 on partialOmega; where p > 1 and Omega is a smooth bounded domain of R^2. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of (Ep), as p o+infty. Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p o+infty, and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in R^2.
Asymptotic analysis and sign changing bubble towers for Lane-Emden problems / DE MARCHIS, Francesca; Ianni, Isabella; Pacella, Filomena. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 17:8(2015), pp. 2037-2068. [10.4171/JEMS/549]
Asymptotic analysis and sign changing bubble towers for Lane-Emden problems
DE MARCHIS, FRANCESCA;IANNI, ISABELLA;PACELLA, Filomena
2015
Abstract
We consider the semilinear Lane-Emden problem (Ep) -Delta u = |u|^{p−1} u in Omega; u = 0 on partialOmega; where p > 1 and Omega is a smooth bounded domain of R^2. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of (Ep), as p o+infty. Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p o+infty, and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in R^2.| File | Dimensione | Formato | |
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