Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems

De Marchis, Francesca, Ianni, Isabella, and Pacella, Filomena. "Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems." Journal of the European Mathematical Society 017.8 (2015): 2037-2068. <http://eudml.org/doc/277352>.

@article{DeMarchis2015,
abstract = {We consider the semilinear Lane–Emden problem \begin\{equation\}\left\lbrace \begin\{array\}\{lr\}-\Delta u= |u|^\{p-1\}u\qquad \mbox\{ in \}\Omega \\ u=0\qquad \qquad \qquad \mbox\{ on \}\partial \Omega \end\{array\}\right.\mathcal \{E\}\_p \end\{equation\} where $p>1$ and $\Omega $ is a smooth bounded domain of $\mathbb \{R\}^2$. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of $(_p)$, as $p\rightarrow +\infty $. Among other results we show, under some symmetry assumptions on $\Omega $, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as $p\rightarrow +\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 $\mathbb \{R\}^2$.},
author = {De Marchis, Francesca, Ianni, Isabella, Pacella, Filomena},
journal = {Journal of the European Mathematical Society},
keywords = {superlinear elliptic boundary value problems; sign-changing solutions; asymptotic analysis; bubble towers; Lane-Emden problems; Lane-Emden problems; sign-changing solutions; asymptotic analysis; bubble towers; superlinear elliptic boundary value problems},
language = {eng},
number = {8},
pages = {2037-2068},
publisher = {European Mathematical Society Publishing House},
title = {Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems},
url = {http://eudml.org/doc/277352},
volume = {017},
year = {2015},
}

TY - JOUR
AU - De Marchis, Francesca
AU - Ianni, Isabella
AU - Pacella, Filomena
TI - Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 8
SP - 2037
EP - 2068
AB - We consider the semilinear Lane–Emden problem \begin{equation}\left\lbrace \begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }\Omega \\ u=0\qquad \qquad \qquad \mbox{ on }\partial \Omega \end{array}\right.\mathcal {E}_p \end{equation} where $p>1$ and $\Omega $ is a smooth bounded domain of $\mathbb {R}^2$. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of $(_p)$, as $p\rightarrow +\infty $. Among other results we show, under some symmetry assumptions on $\Omega $, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as $p\rightarrow +\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 $\mathbb {R}^2$.
LA - eng
KW - superlinear elliptic boundary value problems; sign-changing solutions; asymptotic analysis; bubble towers; Lane-Emden problems; Lane-Emden problems; sign-changing solutions; asymptotic analysis; bubble towers; superlinear elliptic boundary value problems
UR - http://eudml.org/doc/277352
ER -