Liouville Theorem for Quasilinear Elliptic Equations in ℝN

Wangzhe Wu; Qiqi Zhang

doi:10.1007/s11464-024-0014-8

Frontiers of Mathematics ›› 2025, Vol. 20 ›› Issue (5) : 979 -1005. DOI: 10.1007/s11464-024-0014-8

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Liouville Theorem for Quasilinear Elliptic Equations in ℝ^N

Wangzhe Wu ¹
, Qiqi Zhang ²^,^a

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Abstract

We prove Liouville theorem for the equation Δ_mv + v^p + 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.

Keywords

Liouville theorem / quasilinear elliptic equation / p-Laplacian / 35J62

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Wangzhe Wu, Qiqi Zhang. Liouville Theorem for Quasilinear Elliptic Equations in ℝ^N. Frontiers of Mathematics, 2025, 20(5): 979-1005 DOI:10.1007/s11464-024-0014-8