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Peer-reviewedCC BY 4.0Mathematics

Liouville Theorems for Stable Solutions to Anisotropic Quasilinear Equations

  • Ji Huang1
  • Qiqi Zhang1
  • Luofan Zhu1
  1. 1College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China
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Abstract

We consider possibly unbounded and sign-changing stable weak solutions of −ΔmHu+|x|b|u|q−1u=|x|a|u|p−1u in Rn, where m≥2, 1≤q≤m−1<p, and H is a uniformly convex, positively one-homogeneous function. We prove Liouville theorems under explicit dimensional conditions and under integral, pointwise, or gradient growth assumptions. When H(ξ)=|ξ|, the results reduce to the corresponding weighted m-Laplace conclusions.

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Cite

BibTeXRIS
BibTeX
@article{huang2026liouville,
  title = {{Liouville Theorems for Stable Solutions to Anisotropic Quasilinear Equations}},
  author = {Ji Huang and Qiqi Zhang and Luofan Zhu},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203644},
  url = {https://www.mdpi.com/2227-7390/14/20/3644},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Liouville Theorems for Stable Solutions to Anisotropic Quasilinear Equations
AU  - Ji Huang
AU  - Qiqi Zhang
AU  - Luofan Zhu
PY  - 2026
DA  - 2026/10/09
JO  - Mathematics
DO  - 10.3390/math14203644
UR  - https://www.mdpi.com/2227-7390/14/20/3644
AB  - We consider possibly unbounded and sign-changing stable weak solutions of −ΔmHu+|x|b|u|q−1u=|x|a|u|p−1u in Rn, where m≥2, 1≤q≤m−1<p, and H is a uniformly convex, positively one-homogeneous function. We prove Liouville theorems under explicit dimensional conditions and under integral, pointwise, or gradient growth assumptions. When H(ξ)=|ξ|, the results reduce to the corresponding weighted m-Laplace conclusions.
SN  - 2227-7390
ER  -