@article{Zeng2025, 
author = {Fanqi Zeng and Jin Ban and Peilong Dong and Xiaoqin Ma},
title = {Liouville-type theorems for positive solutions to        Δ                  p        1            ,      ⋯      ,              p        r              v  +  f  (  v  )  =  0 in              R              m},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {10},
pages = {5990-6011},
keywords = {Liouville-type theorems, (p1, ⋯, pr)-Laplacian, nonlinear elliptic equations},
url = {https://www.sciopen.com/article/10.3934/era.2025266},
doi = {10.3934/era.2025266},
abstract = {In this paper, we employed the Bernstein method to prove some Liouville-type theorems of the equation        Δ                  p        1            ,      ⋯      ,              p        r              v  +  f  (  v  )  =  0. Here,        Δ                  p        1            ,      ⋯      ,              p        r              v  :=      d    i    v    (      ∑          i      =      1        r        |    ∇  v            |                      p        i            −      2        ∇  v  ). This could be regarded as a natural generalization of the    p-Laplacian and the    (  p  ,  q  )-Laplacian. As applications, we derived Liouville-type theorems of positive solutions to some generalized static Fisher-KPP equation, Allen-Cahn equation, static Newell-Whitehead equation, and Lichnerowicz equation.}
}