In this paper, our main purpose is to consider the quasilinear elliptic equation $$div(|{ abla}u|^{p-2}{ abla}u)=(p-1)f(u)$$ on a bounded smooth domain ${Omega};{subset};R^N$, where p > 1, N > 1 and f is a smooth, increasing function in [0, ${infty}$). We get some estimates of a solution u satisfying $u(x){ ightarrow}{infty}$ as $d(x,;{partial}{Omega}){ ightarrow}0$ under different conditions on f.