English

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.

Keywords

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}
}
R2 v1 2026-06-21T08:27:04.442Z