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

Francesca De Marchis; Isabella Ianni; Filomena Pacella

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 8, page 2037-2068
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topDe 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.