The author studies the entire solutions of non-homogeneous quasilinear elliptic equations for which the following two may serve as typical examples: \[ \begin{aligned} \Delta_pu\equiv \text{div}(|Du|^{p-2}Du) &=f(u), \quad p>1,\;x\in\mathbb R^n, \tag{1}\\ \text{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) &=f(u), \quad x\in\mathbb R^n. \tag{2} \end{aligned} \] As one of the main result, with a comparison lemma introduced in the paper, it is proved that given a \(C^1\) entire distribution solution \(u\) of the equation \(\Delta_pu=a(x) |u|^{q-1}u\), where \(x\in\mathbb R^n\), \(p>1\), \(0