Work

Sufficient conditions for multiplicity and uniqueness of positive solutions of the Hénon equation

Year: 2026

Type: preprint

Abstract: We establish explicit sufficient conditions for multiplicity of positive solutions of the Hénon equation in the unit ball and for uniqueness in one dimension. In the Sobolev-subcritical range, a spherical harmonic function argument shows that the radial solution has Morse index greater than one and therefore differs from a ground state. In even dimensions, a degree-four perturbation in a symmetry and monotonicity cone yields a sufficient condition for nonradiality in the supercritical range. The one-dimensional uniqueness criterion follows from a comparison of weighted Dirichlet eigenvalues and a concavity estimate.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.18039

Author: Du, Geyang

Institution: Jiangnan University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: East China Normal University, Peking University, Xiamen University, Fundamental Research Funds for the Central Universities

OpenAlex ID: W7213492799

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