  The quasi-static solutions of the matter density perturbation in $F(R)$
gravity models have been investigated in numerous papers. However, the
oscillating solutions in $F(R)$ gravity models have not been investigated
enough so far. In this paper, the oscillating solutions are also examined by
using appropriate approximations. And the behaviors of the matter density
perturbation in F(R) gravity models with singular evolutions of the physical
parameters are shortly investigated as applications of the approximated
calculations.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology