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Research Article | Open Access

Liouville type theorems for a class of semilinear biharmonic equations

School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, China
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Abstract

In this paper, motivated by the techniques developed in X. N. Ma et al., arXiv Preprint, 2025, we proved Liouville type theorems for a class of semi-linear biharmonic equations. The proof was based on a differential identity constructed via the invariant tensor method. We combined this identity with an integral estimate to complete the proof.

Keywords

semilinear biharmonic equationsLiouville type theoremsinvariant tensors
CLC number: 35B45, 35J60

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 7529-7542
DOI: 10.3934/math.2026308

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Ma Y. Liouville type theorems for a class of semilinear biharmonic equations. AIMS Mathematics, 2026, 11(3): 7529-7542. https://doi.org/10.3934/math.2026308

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Received: 10 December 2025
Revised: 10 March 2026
Accepted: 18 March 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)