Low-mass condensations (LMCs) are observed inside the envelope of the collapsing molecular cloud cores. In this research, we investigate the effects of landing LMCs for occurrence of instability through the protostellar accretion disks. We consider some regions of the disk where duration of infalling and landing of the LMCs are shorter than the orbital period. In this way, we can consider the landing LMCs as density bumps and grooves in the azimuthal direction of an initial thin axisymmetric steady state self-gravitating protostellar accretion disk (nearly Keplerian). Using the linear effects of the bump quantities, we obtain a characteristic equation for growth/decay rate of bumps; we numerically solve it to find occurrence of instability. We also evaluate the minimum-growth-time-scale (MGTS) and the enhanced mass accretion rate. The results show that infalling and landing of the LMCs in the inner regions of the protostellar accretion disks can cause faster unstable modes and less enhanced accretion rates relative to the outer regions. Also, more fragmentation of landed LMCs in the azimuthal direction have less chance for instability, and then can produce more values of enhanced mass accretion rate.
