Nodal radial solutions for a zero-mass (p,q)-Laplacian equation with Hardy-Hénon type weight
Abstract
We establish the existence of radial nodal solutions for a class of zero-mass (p,q)-Laplacian equations in ℝN with a Hardy-Hénon type weight |x|α. The absence of lower-order potential terms motivates the use of a homogeneous radial variational framework adapted to the mixed p- and q-growth structure. A key ingredient is a weighted Sobolev embedding theorem that establishes continuity and compactness in the appropriate range of exponents and identifies the sharp interval for continuous embedding. Building on these results, we construct sign-changing radial solutions through a variational method based on radial partitions and critical levels. The main result asserts that, for every k∈ℕ, the problem admits a radial weak solution with exactly k nodal zeros. The proof combines minimization on Nehari manifolds over radial subdomains with an optimization procedure that determines the nodal radii and ensures the compatibility of the solution across nodal interfaces.
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BibTeX
@misc{albuquerque2026nodal,
title = {{Nodal radial solutions for a zero-mass $(p,q)$-Laplacian equation with Hardy-Hénon type weight}},
author = {José Carlos de Albuquerque and Jonison Carvalho and Eudes Barboza},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39063},
eprint = {2610.39063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39063},
}
RIS
TY - UNPB
TI - Nodal radial solutions for a zero-mass (p,q)-Laplacian equation with Hardy-Hénon type weight
AU - José Carlos de Albuquerque
AU - Jonison Carvalho
AU - Eudes Barboza
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.39063
UR - https://arxiv.org/abs/2610.39063
AB - We establish the existence of radial nodal solutions for a class of zero-mass (p,q)-Laplacian equations in ℝ^N with a Hardy-Hénon type weight |x|^α. The absence of lower-order potential terms motivates the use of a homogeneous radial variational framework adapted to the mixed p- and q-growth structure. A key ingredient is a weighted Sobolev embedding theorem that establishes continuity and compactness in the appropriate range of exponents and identifies the sharp interval for continuous embedding. Building on these results, we construct sign-changing radial solutions through a variational method based on radial partitions and critical levels. The main result asserts that, for every k∈ℕ, the problem admits a radial weak solution with exactly k nodal zeros. The proof combines minimization on Nehari manifolds over radial subdomains with an optimization procedure that determines the nodal radii and ensures the compatibility of the solution across nodal interfaces.
ER -