  In this paper, we would like to examine whether stable de Sitter inflationary
solutions appear within power-law extensions of the Starobinsky model. In
particular, we will address general constraints for the existence along with
the stability of de Sitter inflationary solutions in a general case involving
not only the Starobinsky $R^2$ term but also an additional power-law $R^n$ one.
According to the obtained results, we will be able to identify which extension
is more suitable for an early inflationary phase rather than a late-time cosmic
acceleration phase. To be more specific, we will consider several values of $n$
to see whether the corresponding de Sitter inflationary solutions are stable or
not.
