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arXiv · 2607.07631

Analysis of an Emden-Fowler-H\'enon type equation

Pablo dos Santos Corrêa Junior·Ederson Moreira dos Santos·Delia Schiera
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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.

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Pablo dos Santos Corrêa Junior, Ederson Moreira dos Santos, Delia Schiera. 2026-07-08. Analysis of an Emden-Fowler-H\'enon type equation. https://arxiv.org/abs/2607.07631

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