  We investigate when does the Repov\v{s}-Semenov Splitting problem for
selections have an affirmative solution for continuous set-valued mappings in
finite-dimensional Banach spaces. We prove that this happens when images of
set-valued mappings or even their graphs are P-sets (in the sense of Balashov)
or strictly convex sets. We also consider an example which shows that there is
no affirmative solution of this problem even in the simplest case in $\R^{3}$.
We also obtain affirmative solution of the Approximate splitting problem for
Lipschitz continuous selections in the Hilbert space.
