Asymptotic analysis and sign changing bubble towers for Lane-Emden problems
Analysis of PDEs
2016-01-19 v2
Abstract
We consider the semilinear Lane-Emden problem in a smooth bounded domain of the plane. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions as the exponent p of the nonlinearity goes to infinity. Among other results we show, under some symmetry assumptions on the domain, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p goes to infinity, 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 the plane.
Keywords
Cite
@article{arxiv.1309.6961,
title = {Asymptotic analysis and sign changing bubble towers for Lane-Emden problems},
author = {Francesca De Marchis and Isabella Ianni and Filomena Pacella},
journal= {arXiv preprint arXiv:1309.6961},
year = {2016}
}