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This is a Quantitative Study study.

October 16, 2025Open Access

A priori estimates of stable solutions of the general Hardy-Henon equation in the ball

Key Points

Semi-stable radial solutions of the Hardy-Henon equation exist in bounded and unbounded forms, offering valuable insights.
The established bounds for solutions hold for dimensions between 2 and 10+4α, enhancing understanding of the equation.
Sharp pointwise estimates are provided for higher dimensions, improving the theoretical framework for semi-stable solutions.
A diverse family of semi-stable unbounded solutions is identified, which could have significant implications in applied contexts.

Abstract

This paper is devoted to the study of semi-stable radial solutions u H¹ (B₁) of -Δu= x^αf (u) in B₁0, where f C¹ (R) is a general nonlinearity, α>-2 and B₁ is the unit ball of RN, N>1. We establish the boudness of such solutions for dimensions 2 N<10+4α and sharp pointwise estimates in the case N10+4α. In addition, we provide, for this range of dimensions, a large family of semi-stable radially decreasing unbounded H¹ (B₁) solutions.

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Martínez-Baena et al. (Thu,) studied this question.

www.synapsesocial.com/papers/68f04acce559138a1a06e99b — DOI: https://doi.org/10.48550/arxiv.2506.21515

Authors

J. Silverio Martínez-Baena

Salvador Villegas

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A priori estimates of stable solutions of the general Hardy-Henon equation in the ball

Key Points

Abstract

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Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion