Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems
Francesca De Marchis
Università di Roma Tor Vergata, ItalyIsabella Ianni
Seconda Università di Napoli, Caserta, ItalyFilomena Pacella
Università di Roma La Sapienza, Italy
![Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-17-issue-8.png&w=3840&q=90)
Abstract
We consider the semilinear Lane–Emden problem
where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of (), as . 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 , 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 .
Cite this article
Francesca De Marchis, Isabella Ianni, Filomena Pacella, Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems. J. Eur. Math. Soc. 17 (2015), no. 8, pp. 2037–2068
DOI 10.4171/JEMS/549