Geometric uniqueness of positive radial solutions for singular p-Laplacian equations on annuli
Year: 2026
Type: article
Abstract: We prove uniqueness results for positive radial Dirichlet problems for the \(p\)-Laplacian on annuli in the singular range \(1<p<2\) and when \( p=2. \) For the Lane--Emden equation \( -\Delta_p u=u^{q-1}, \) uniqueness holds for every \(q\ge2\) with \(q>p,\) up to and including the critical Sobolev exponent when \(n>p.\) We also show that uniqueness persists under sufficiently small weighted \(C^1\) perturbations of the pure power in the strictly subcritical range. The proof is geometric: varying the initial momentum at the inner boundary produces a shooting curve in the \((u,w)\)-plane, and uniqueness follows by proving that this curve meets the outer boundary condition transversely. For the pure power, transversality follows from an exact scaling determinant and a Pohozaev-type trapping estimate. Under perturbation, a quantitative determinant bound preserves the same geometric mechanism.
Author: Bevin Maultsby
Institution: North Carolina State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7169780322