Existence and symmetry breaking results for a Hénon-type equation with Grushin operator

Abstract In this paper, we consider a Hénon-type equation for the Grushin operator. After proving a radial lemma, we establish the existence of a solution for a superlinear and supercritical problem. Additionally, we derive a symmetry-breaking result for ground-state solutions in the subcritical case.

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Publication Details

Journal
Proceedings of the Royal Society of Edinburgh Section A Mathematics
Published
2025-11-05
DOI
https://doi.org/10.1017/prm.2025.10076
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Existence and symmetry breaking results for a Hénon-type equation with Grushin operator

Marcelo F. Furtado
Proceedings of the Royal Society of Edinburgh Section A Mathematics
Nonlinear Partial Differential Equations
article

Existence and symmetry breaking results for a Hénon-type equation with Grushin operator

Marcelo F. Furtado
article en

Abstract

Abstract In this paper, we consider a Hénon-type equation for the Grushin operator. After proving a radial lemma, we establish the existence of a solution for a superlinear and supercritical problem. Additionally, we derive a symmetry-breaking result for ground-state solutions in the subcritical case.

Proceedings of the Royal Society of Edinburgh Section A Mathematics
Universidade de Brasília (BR)
Openalex Percentile: Top 55%
Nonlinear Partial Differential Equations
DOISourceOpenAlex
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Existence and symmetry breaking results for a Hénon-type equation with Grushin operator — Marcelo F. Furtado · Proceedings of the Royal Society of Edinburgh Section A Mathematics (2025) | TGRS Research Map | TGRS