Summary: Let \(X_j\), \(j=1,\dots,k\), be first-order smooth quasi-homogeneous vector fields on \(\mathbb{R}^n\) with the property that the dimension of the Lie algebra generated by these vector fields is \(n\) at \(x=0\) and \(X^*_j=-X_j\), \(j=1,\dots,k\). Let \(L=\sum^k_{i=1}X_i^2\). We study the nonnegative solutions of the semilinear equation \[ Lu+f(x,u)=0\text{ (or }\leq 0) \] in \(\mathbb{R}^n\) and generalized cone domain, respectively, and prove that the solutions must be vanish under some suitable conditions.