Analysis of an Emden-Fowler-Hénon type equation

Pablo dos Santos Corrêa Junior; Ederson Moreira dos Santos; Delia Schiera

Analysis of an Emden-Fowler-Hénon type equation

Analysis of PDEs 2026-07-08 v1

Authors: Pablo dos Santos Corrêa Junior , Ederson Moreira dos Santos , Delia Schiera

Abstract

This work investigates a H\'enon-type equation with the cap-shaped weight $V_{\alpha}(|x|)=(4|x|(1-|x|))^\alpha$ , which concentrates on the sphere of radius $1/2$ as $\alpha\to\infty$ . Particular attention is devoted to ground state solutions and the phenomenon of symmetry breaking in the large- $\alpha$ regime. A complete description of the asymptotic behavior of ground state radial solutions is obtained as $\alpha\to\infty$ . The analytical results are further supported by numerical simulations of the radial ground states.

Keywords

Henon equation ground states symmetry breaking asymptotic behavior radial solutions weighted nonlinearity

Cite

@article{arxiv.2607.07631,
  title  = {Analysis of an Emden-Fowler-Hénon type equation},
  author = {Pablo dos Santos Corrêa Junior and Ederson Moreira dos Santos and Delia Schiera},
  journal= {arXiv preprint arXiv:2607.07631},
  year   = {2026}
}