Liouville Theorem for $(p,q)$-Laplace Equations

Yang Zhou; Hua Zhu

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arXiv · 2606.20033

Liouville Theorem for $(p,q)$-Laplace Equations

Yang Zhou·Hua Zhu

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Abstract

We employ the vector field method to establish a Liouville-type theorem for a class of $(p,q)$-Laplace equations in the Euclidean space $\mathbb{R}^n$. By modifying the exponents in the differential identity, we prove nonexistence in the subcritical range $p-1<\alpha<q^*-1$, where $q^*=nq/(n-q)$. The approach relies on constructing a suitable differential identity, carrying out precise integral estimates with cutoff functions, and combining sign control and decay of the cutoff errors.

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Yang Zhou, Hua Zhu. 2026-06-18. Liouville Theorem for $(p,q)$-Laplace Equations. https://arxiv.org/abs/2606.20033

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