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On Liouville problems for (p,q)-Laplacian inequalities on Finsler measure spaces
Abstract
We study the Liouville property for nonnegative weak solutions of the (p,q)-Laplacian elliptic differential inequality Δmpu(x)+Δmqu(x)+V(x)us(x)≤ 0 and the associated parabolic differential inequality ∂t u(x,t) ≥ Δmpu(x,t)+Δmqu(x,t)+V(x,t)us(x,t) on a forward geodesically complete noncompact Finsler measure space (M,F,m) with finite reversibility. Under several sets of integral growth conditions on the positive potential function over certain annular domains, we prove that any nonnegative weak solution vanishes almost everywhere. The proofs of our results are essentially based on the nonlinear capacity method.
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BibTeX
@misc{wang2026liouville,
title = {{On Liouville problems for $(p,q)$-Laplacian inequalities on Finsler measure spaces}},
author = {Tiancheng Wang and Changwei Xiong and Dongjie Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04780},
eprint = {2609.04780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04780},
}
RIS
TY - UNPB
TI - On Liouville problems for (p,q)-Laplacian inequalities on Finsler measure spaces
AU - Tiancheng Wang
AU - Changwei Xiong
AU - Dongjie Zhao
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04780
UR - https://arxiv.org/abs/2609.04780
AB - We study the Liouville property for nonnegative weak solutions of the (p,q)-Laplacian elliptic differential inequality Δ^m_pu(x)+Δ^m_qu(x)+V(x)u^s(x)≤ 0 and the associated parabolic differential inequality ∂_t u(x,t) ≥ Δ^m_pu(x,t)+Δ^m_qu(x,t)+V(x,t)u^s(x,t) on a forward geodesically complete noncompact Finsler measure space (M,F,m) with finite reversibility. Under several sets of integral growth conditions on the positive potential function over certain annular domains, we prove that any nonnegative weak solution vanishes almost everywhere. The proofs of our results are essentially based on the nonlinear capacity method.
ER -