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<p>We prove Liouville theorem for the equation Δ<sub><i>m</i></sub><i>v</i> + <i>v</i><sup><i>p</i></sup> + <i>M</i>∣∇<i>v</i>∣<sup><i>q</i></sup> = 0 in a domain Ω ⊂ ℝ<sup><i>n</i></sup>, with <i>M</i> ∈ ℝ in the critical and subcritical case. As a natural extension of our recent work [2023, arXiv:2311.04641], the proof is based on an integral identity and Young’s inequality.</p>

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Liouville Theorem for Quasilinear Elliptic Equations in ℝN

  • 期刊论文

  • 发表日期：

    2025年1月5日

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  • Wangzhe Wu,
  • Qiqi Zhang

摘要

We prove Liouville theorem for the equation Δmv + vp + M∣∇v∣q = 0 in a domain Ω ⊂ ℝn, with M ∈ ℝ in the critical and subcritical case. As a natural extension of our recent work [2023, arXiv:2311.04641], the proof is based on an integral identity and Young’s inequality.