Multiple Solutions for a Henon-Like Equation on the Annulus
Analysis of PDEs
2008-06-10 v2
Abstract
For the equation (-\Delta u = | |x|-2 |^\alpha u^{p-1}), (1 < |x| < 3), we prove the existence of two solutions for (\alpha) large, and of two additional solutions when (p) is close to the critical Sobolev exponent (2^*=2N/(N-2)). A symmetry--breaking phenomenon appears, showing that the least--energy solutions cannot be radial functions.
Cite
@article{arxiv.0705.1492,
title = {Multiple Solutions for a Henon-Like Equation on the Annulus},
author = {Marta Calanchi and Simone Secchi and Elide Terraneo},
journal= {arXiv preprint arXiv:0705.1492},
year = {2008}
}