Summary: We present some oscillation criteria for the second order differential equation of the form \[ (r(t)x'(t))'+p(t)x'(t)+q(t)x(t)+\sum^n_{j=1}q_j (t)|x^{\alpha_j}(t)|\text{sgn}\,x(t)=e(t),\;t\geq 0 \] where \(r(t)\in C^1[0, \infty),p(t),q(t),q_j(t),e(t),e(t)\in C[0,\infty)\), \(r(t)>0\), \(\alpha_1> \cdots>\alpha_m>1>\alpha_{m+1}>\cdots>\alpha_n>0\) \((n>m\geq 1)\) without assuming that \(p(t)\), \(q(t)\), \(q_j(t)\) and \(e(t)\) are nonnegative. In particular, for \(n=1\), we obtain some new oscillation criteria. The results obtained in this paper extend and improve some of the existing results.