  Existence and uniqueness of mass-conserving classical solutions to the
continuous coagulation equation with collisional breakage are investigated for
an unbounded class of collision kernels and a particular case of the
distribution function. The distribution function may have a possibility to
attain singularity at the origin. The proof of the existence result relies on
the compactness method. Moreover, a uniqueness result is shown. In addition, it
is observed that the uniqueness solution is mass-conserving.
