TY - JOUR
T1 - Liouville Type Theorems of Semilinear Equations with Square Sum of Vector Fields
AU - Yazhou Han , Xuebo Luo  & Pengcheng Niu 
JO - Journal of Partial Differential Equations
VL - 2
SP - 149
EP - 153
PY - 2005
DA - 2005/05
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5351.html
KW - Liouville type theorem
KW - superlinear equation
KW - local Hörmander condition
KW - square sum operator
KW - generalized cone domain
AB -  Let X_j ; j = 1, …, k, be first order smooth quasi-homogeneous vector fields on Rn with the property that the dimension of the Lie algebra generated by these vector fields is n at x = 0 and X^∗_j = -X_j, j = 1, …, k. Let L = \sum^k_{i=1} X²_i . In this paper, we study the nonnegative solutions of semilinear equation Lu + f(x, u) = 0 (or ≤ 0 ) in Rn and generalized cone domain, respectively, and prove that the solutions must be vanish under some suitable conditions.